Filed Pursuant to Rule 424(b)(3)

Registration No. 333-294316

Prospectus Supplement
(to Prospectus dated March 23, 2026)

PRESIDIO PRODUCTION COMPANY

11,887,469 SHARES OF CLASS A COMMON STOCK ISSUABLE

UPON THE EXERCISE OF WARRANTS

133,332 WARRANTS

29,757,255 SHARES OF CLASS A COMMON STOCK

This Prospectus Supplement updates and supplements the prospectus dated March 23, 2026 (the “Prospectus”), which forms a part of our registration statement on Form S-1 (No. 333-294316). This prospectus supplement is being filed to update and supplement the information in the Prospectus with the information contained in our Current Report on Form 8-K, filed with the Securities and Exchange Commission on May 14, 2026 (the “Current Report”). Accordingly, we have attached the Current Report to this Prospectus Supplement.

The Prospectus and this Prospectus Supplement relates to the issuance by Presidio Production Company (“Presidio” or the “Company”) of up to 11,887,469 shares of Class A Common Stock, par value $0.0001 (the “Presidio Class A Common Stock”) that may be issued upon the exercise of the Presidio Warrants (as defined below) and the offer and sale from time to time by the selling securityholders named in the Prospectus and this Prospectus Supplement (the “Selling Securityholders”), or their permitted transferees, of up to 29,757,255 shares of Presidio Class A Common Stock and up to 133,332 Presidio Warrants.

The 11,887,469 shares of Presidio Class A Common Stock that may be issued upon the exercise of the Presidio Warrants that the Prospectus and this Prospectus Supplement relates to include: (i) up to 11,666,637 shares of Presidio Class A Common Stock that may be issued upon the exercise of 11,666,637 warrants to purchase Presidio Class A Common Stock at an exercise price of $11.50 per share (the “Public Warrants”) and (ii) up to 220,832 shares of Presidio Class A Common Stock that may be issued upon the exercise of 220,832 warrants to purchase Presidio Class A Common Stock at an exercise price of $11.50 per share (the “Private Placement Warrants” and together with the Public Warrants, the “Presidio Warrants”).

The shares of Presidio Class A Common Stock and Presidio Warrants offered for resale under the Prospectus and this Prospectus Supplement were issued to the Selling Securityholders (as applicable to each) in accordance with the terms of, and transactions contemplated by, the Business Combination Agreement, dated as of August 5, 2025 (the “Business Combination Agreement”), by and among Presidio MidCo Inc., a Delaware corporation (formerly EQV Ventures Acquisition Corp., a Cayman Islands exempted company) (“EQV”), Presidio (f/k/a Presidio PubCo Inc.), Prometheus PubCo Merger Sub Inc., a Delaware corporation and a direct, wholly owned subsidiary of Presidio (“EQV Merger Sub”), Prometheus Holdings LLC, a Delaware limited liability company and a direct, wholly owned subsidiary of EQV (“Prometheus Holdings”), Prometheus Merger Sub LLC, a Delaware limited liability company and a direct, wholly owned subsidiary of Prometheus Holdings (“Presidio Merger Sub”) and Presidio Investment Holdings LLC, a Delaware limited liability company (“PIH”). The Presidio Class A Common Stock registered hereunder represents the securities issued to the Selling Securityholders pursuant to the terms of the Business Combination Agreement, as applicable to each Selling Securityholder, concurrently with the closing of the transactions contemplated by the Business Combination Agreement (the “Business Combination”).

The Business Combination is described in greater detail in the Prospectus. See “Prospectus Summary — The Business Combination.”

The 29,757,255 maximum number of shares of Presidio Class A Common Stock offered for resale under the Prospectus and this Prospectus Supplement consists of: (a) 7,686,960 shares of Presidio Class A Common Stock that were issued to EQV Ventures Sponsor LLC, a Delaware limited liability company, and its affiliates (the “Sponsor”) upon the conversion of 282,314 EQV Class A Shares and 7,404,646 EQV Class B Shares, (b) 160,000 shares of Presidio Class A Common Stock that were issued to the former independent directors of EQV, upon the conversion of 160,000 EQV Class A Shares, (c) 120,000 shares of Presidio Class A Common Stock that were issued to the former independent directors of EQV, upon the conversion of 120,000 EQV Class A Shares, (d) 9,315,217 shares of Presidio Class A Common Stock that were issued in connection with the PIPE Financing (as defined in the Prospectus), (e) 2,717,300 shares of Presidio Class A Common Stock that may be issued upon the conversion of the 27,173 shares of Series B Preferred Stock, (f) 937,500 shares of Presidio Class A Common Stock that may be issued upon the exercise of warrants to purchase Presidio Class A Common Stock at an exercise price of $0.01 per share and (g) 8,806,946 shares of Presidio Class A Common Stock issued, or that may be issued upon the conversion of Prometheus Holdings Common Units (as defined in the Prospectus), to certain of the other Selling Securityholders named herein in connection with the Business Combination as merger consideration.

There are approximately 27,652,068 outstanding shares of Presidio Class A Common Stock as of the date of the Prospectus and this Prospectus Supplement. Given the substantial number of shares of Presidio Class A Common Stock being registered for potential resale by Selling Securityholders pursuant to the Prospectus and this Prospectus Supplement, the sale of shares by the Selling Securityholders, or the perception in the market that the Selling Securityholders intend to sell shares, could increase the volatility of the market price of Presidio Class A Common Stock or result in a significant decline in the public trading price of the Presidio Class A Common Stock. Even if the current trading price of the Presidio Class A Common Stock is close to the price at which the units were initially issued in EQV’s initial public offering, certain Selling Securityholders may have an incentive to sell because they will still profit on sales due to the lower price at which they purchased their shares compared to the public investors. The public securityholders may not experience a similar rate of return on the securities they purchase due to differences in the purchase prices and the current trading price.

Pursuant to the Prospectus and this Prospectus Supplement, the Selling Securityholders are permitted to offer the securities from time to time, if and to the extent as they may determine, through public or private transactions or through other means described in the section of the Prospectus entitled “Plan of Distribution” at prevailing market prices, at prices different than prevailing market prices or at privately negotiated prices. The Selling Securityholders may sell shares through agents they select or through underwriters and dealers they select. The Selling Securityholders also may sell their securities directly to investors. If the Selling Securityholders use agents, underwriters or dealers to sell their securities, we will name such agents, underwriters or dealers and describe any applicable commissions or discounts in a supplement to the Prospectus and this Prospectus Supplement if required.

Certain of the securities registered hereby remain subject to contractual transfer restrictions described under “Certain Relationships and Related Person Transactions” in the Prospectus and may not be sold until such restrictions lapse.

We have agreed to bear all of the expenses incurred in connection with the registration of these securities. The Selling Securityholders will pay or assume underwriting fees, discounts and commissions or similar charges, if any, incurred in the sale of securities by them.

The Selling Securityholders identified in the Prospectus and this Prospectus Supplement may offer, sell or distribute all or a portion of the Presidio Class A Common Stock included under the Prospectus and this Prospectus Supplement (as applicable to each Selling Securityholder) in the section entitled “Selling Securityholders.” We will not receive any proceeds from the sale of securities by the Selling Securityholders. However, we may receive proceeds from the exercise of the Presidio Warrants and the Series A Preferred Investor Warrants to the extent any such warrants are exercised for cash. The exercise price of the Presidio Warrants is $11.50 per share, and the exercise price of the Series A Preferred Investor Warrants is $0.01 per share. We believe the likelihood that warrant holders will exercise their warrants, and therefore the amount of cash proceeds that we would receive, is dependent upon the trading price of the Presidio Class A Common Stock. If the trading price for the Presidio Class A Common Stock ever falls below $11.50 per share, we believe holders of Presidio Warrants would be unlikely to exercise their warrants.

We may amend or supplement the Prospectus and this Prospectus Supplement from time to time by filing amendments or supplements as required.

The Presidio Class A Common Stock and the Public Warrants are listed on the New York Stock Exchange under the symbols “FTW” and “FTW WS,” respectively. On May 13, 2026, the closing price of the Presidio Class A Common Stock was $11.12 per share, and the closing price of the Public Warrants on May 13, 2026 was $1.095 per warrant.

This Prospectus Supplement updates and supplements the information in the Prospectus and is not complete without, and may not be delivered or utilized except in combination with, the Prospectus, including any subsequent amendments or supplements thereto. This Prospectus Supplement should be read in conjunction with the Prospectus, and if there is any inconsistency between the information in the Prospectus and this Prospectus Supplement, you should rely on the information in this Prospectus Supplement. The information in this Prospectus Supplement modifies and supersedes, in part, the information in the Prospectus. Any information in the Prospectus that is modified or superseded shall not be deemed to constitute a part of the Prospectus except as modified or superseded by this Prospectus Supplement. You should not assume that the information provided in this Prospectus Supplement or the Prospectus is accurate as of any date other than their respective dates. Neither the delivery of this Prospectus Supplement, the Prospectus nor any sale made hereunder, shall under any circumstances create any implication that there has been no change in our affairs since the date of this Prospectus Supplement, or that the information contained in this Prospectus Supplement, the Prospectus is correct as of any time after the date of that information.

We are an “emerging growth company” and a “smaller reporting company” as those terms are defined under applicable federal securities laws, and as such, are subject to certain reduced public company reporting requirements.

AN INVESTMENT IN OUR COMMON STOCK INVOLVES SIGNIFICANT RISKS. YOU SHOULD CAREFULLY CONSIDER THE RISK FACTORS BEGINNING ON PAGE 13 OF THIS PROSPECTUS BEFORE YOU MAKE YOUR DECISION TO INVEST IN OUR COMMON STOCK.

Neither the Securities and Exchange Commission nor any other regulatory body has approved or disapproved of these securities nor passed upon the accuracy or adequacy of this Prospectus Supplement. Any representation to the contrary is a criminal offense.

The date of this Prospectus Supplement is May 14, 2026.

UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

FORM 8-K

CURRENT REPORT
Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934

Date of Report (Date of earliest event reported): May 7, 2026

PRESIDIO PRODUCTION COMPANY
(Exact name of registrant as specified in its charter)

(800) 461-1604
(Registrant’s telephone number, including area code)

Presidio PubCo Inc.

1090 Center Drive

Park City, UT 84098
(Former name or former address, if changed since last report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions:

Securities registered pursuant to Section 12(b) of the Act:

Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 (§ 230.405 of this chapter) or Rule 12b-2 of the Securities Exchange Act of 1934 (§ 240.12b-2 of this chapter).

Emerging growth company ☒

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. ☐

Item 1.01 Entry into a Material Definitive Agreement.

On May 7, 2026, Presidio Production Company (NYSE: FTW) (“Presidio” or the “Company”) entered into purchase and sale agreements (the “Purchase and Sale Agreements”), by and between each of Canyon Creek Energy – Arkoma, LLC (“Canyon Creek”), Alchemist Energy LeaseCo, LP (“Alchemist”), Pivotal Arkoma Basin II, LLC (“Pivotal”), East Dennis Oil Company, LLC, Harvard Petroleum Company, LLC, FBF Energy, LLC and Harbor Island Management Company, LLC (collectively, the “Seller Parties”) pursuant to which the Company acquired the properties and assets from the Seller Parties set forth in the Purchase and Sale Agreements (the “Purchase and Sale Transaction”) for 2,173,913 shares of the Company’s common stock (the “Share Consideration”), par value $0.0001 per share (“Common Stock”) and $60 million of cash (the “Transaction”). The Purchase and Sale Agreements with Canyon Creek, Alchemist and Pivotal represented approximately $81 million of the total $83 million value. With each Purchase and Sale Agreement, the Company purchased oil and gas leases, oil, gas, and mineral leases and subleases, carried interests, operating rights, record title interests, overriding royalty interests and other interests to the crude oil, gas, casinghead gas, condensate, natural gas liquids, and other gaseous or liquid hydrocarbons (including ethane, propane, iso-butane, nor-butane, gasoline, and scrubber liquids) of any type and chemical composition in, on, under, and that may be produced from or are otherwise attributable to certain properties in Oklahoma (the “Properties”). The Company expects the Transaction to close early in the third quarter of 2026, subject to customary closing conditions. There can be no assurance that all of the conditions to closing the Transaction will be satisfied.

Each Purchase and Sale Agreement contains representations, warranties and other provisions that were made only for purposes of each particular Purchase and Sale Agreement as of specific dates and were solely for the benefit of the parties thereto. Each Purchase and Sale Agreement is a contractual document that establishes and governs the legal relations among the parties thereto and is not intended to be a source of factual, business or operational information about the Company or the Seller Parties or the assets to be acquired from the Seller Parties. The representations and warranties made by the Company and Seller Parties in each Purchase and Sale Agreement may be (i) qualified by disclosure schedules containing information that modifies, qualifies or creates exceptions to such representations and warranties and (ii) subject to standards of materiality applicable to the contracting parties that differ from those applicable to investors. Accordingly, investors and security holders should not rely on such representations and warranties as characterizations of the actual state of facts or circumstances.

The descriptions of the Purchase and Sale Agreements herein does not purport to be complete and is qualified in its entirety by reference to the Purchase and Sale Agreements, when filed with the Securities and Exchange Commission (the “SEC”).

Canyon Creek Acquisition

Pursuant to the Purchase and Sale Agreement between the Company and Canyon Creek (the “Canyon Creek PSA”), the Company agreed to purchase certain Properties for consideration comprising (i) $19.986 million of cash and (ii) 1,166,627 shares of Common Stock (the “Canyon Creek Share Consideration”), each subject to purchase price adjustments and customary closing adjustments. The Canyon Creek PSA contains customary representations and warranties, covenants, termination rights and indemnification provisions for a transaction of this size and nature, provides the parties thereto with specified rights and obligations and allocates risk among them in a customary manner.

Under the Canyon Creek PSA, the Company agreed to enter into a registration rights agreement with Canyon Creek or its designee in connection with the closing of the Canyon Creek Acquisition (the “Canyon Creek Registration Rights Agreement”). Pursuant to the terms of the Canyon Creek Registration Rights Agreement, the Company will agree to register under the Securities Act of 1933, as amended (the “Securities Act”), the resale of the shares of Common Stock to be issued as part of the Canyon Creek Share Consideration and to grant such person certain rights to request and/or participate in underwritten offerings. The foregoing description of the Canyon Creek Registration Rights Agreement does not purport to be complete and is qualified in its entirety by reference to the form of Canyon Creek Registration Rights Agreement included as Exhibit C to the Canyon Creek PSA to be filed with the SEC.

Alchemist Acquisition

Pursuant to the Purchase and Sale Agreement between the Company and Alchemist (the “Alchemist PSA”), the Company agreed to purchase certain Properties for consideration comprising (i) $25.395 million of cash and (ii) 920,109 shares of Common Stock (the “Alchemist Share Consideration”), each subject to purchase price adjustments and customary closing adjustments. The Alchemist PSA contains customary representations and warranties, covenants, termination rights and indemnification provisions for a transaction of this size and nature, provides the parties thereto with specified rights and obligations and allocates risk among them in a customary manner.

Under the Alchemist PSA, the Company agreed to enter into a registration rights agreement with Alchemist or its designee in connection with the closing of the Alchemist Acquisition (the “Alchemist Registration Rights Agreement”). Pursuant to the terms of the Alchemist Registration Rights Agreement, the Company will agree to register under the Securities Act, the resale of the shares of Common Stock to be issued as part of the Alchemist Share Consideration and to grant such person certain rights to request and/or participate in underwritten offerings. This description of the Alchemist Registration Rights Agreement does not purport to be complete and is qualified in its entirety by reference to the form of Alchemist Registration Rights Agreement included as Exhibit C to the Alchemist PSA to be filed with the SEC.

Pivotal Acquisition

Pursuant to the Purchase and Sale Agreement between the Company and Pivotal (the “Pivotal PSA”), the Company agreed to purchase certain Properties for consideration comprising $13.125 million of cash, subject to purchase price adjustments and customary closing adjustments. The Pivotal PSA contains customary representations and warranties, covenants, termination rights and indemnification provisions for a transaction of this size and nature, provides the parties thereto with specified rights and obligations and allocates risk among them in a customary manner.

Cautionary Note Regarding Forward-Looking Statements

Statements in this Current Report on Form 8-K and in our other filings with the SEC, as well as other statements we may make from time to time, other than statements of historical fact, constitute "forward-looking statements" within the meaning of the Private Securities Litigation Reform Act of 1995. In some cases, you can identify forward-looking statements by words such as "may," "will," "should," "expects," "intends," "plans," "anticipates," "believes," "estimates," "guidance," "outlook," "predicts," "potential," "continue," and similar words or phrases or the negative of these words or phrases. These statements relate to future events or the Company’s future financial performance and involve known and unknown risks, uncertainties, and other factors that may cause the Company’s actual results, performance, or achievements to be materially different from any future results, performance or achievements expressed or implied by these forward-looking statements. Although the Company believes the expectations reflected in the forward-looking statements are reasonable when made, the Company cannot guarantee future results, levels of activity, performance, or achievements.  See the Company’s final prospectus and definitive proxy statement filed with the SEC, dated January 30, 2026 in the section entitled “Risk Factors” and the Company’s other filings with the SEC for a discussion of risks and uncertainties. The Company disclaims any obligation to update or revise any forward-looking statements, whether as a result of new information, future events or otherwise.

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.

Dated: May 14, 2026

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