Exhibit 1.2

ALPINE INCOME PROPERTY TRUST, INC.
(a Maryland corporation)

$35,000,000 of Shares of 8.00% Series A Cumulative Redeemable Preferred Stock

(Par Value $0.01)

AMENDMENT NO. 1 TO THE EQUITY DISTRIBUTION AGREEMENT

April 24, 2026

To the addressee set forth above:

Reference is made to the Equity Distribution Agreement, dated December 5, 2025 (the “Agreement”), by and among Alpine Income Property Trust, Inc., a Maryland corporation (the “Company”), Alpine Income Property Manager, LLC, a Delaware limited liability company (the “Adviser”), and Alpine Income Property OP, LP, a Delaware limited partnership (the “Operating Partnership”) and [•] (the “Manager” and, together with the Company, the Adviser and the Operating Partnership, the “Parties”). Capitalized terms used but not defined herein shall have the meaning assigned to them in the Agreement.

In light of the Company’s entry into new Equity Distribution Agreements, dated the date hereof, by and among the Company, the Adviser and the Operating Partnership, and each of Cantor Fitzgerald & Co. and Huntington Securities, Inc., as manager, the Parties desire to amend the Agreement through this Amendment No. 1 to the Equity Distribution Agreement (this “Amendment”) to modify the definition of certain defined terms set forth in the Agreement and used herein and to make certain other changes to the Agreement with effect on and after the date hereof (the “Effective Date”).

1.             Amendments to the Agreement. The Parties agree, from and after the Effective Date, that:

The Company, the Adviser and the Operating Partnership have also entered into separate equity distribution agreements (collectively, as each may be amended from time to time, the “Alternative Distribution Agreements”), dated as of December 5, 2025, as amended on April 24, 2026, with each of Raymond James & Associates, Inc., A.G.P./Alliance Global Partners, Robert W. Baird & Co. Incorporated, B. Riley Securities, Inc., Colliers Securities LLC, Jefferies LLC, JonesTrading Institutional Services LLC, Lucid Capital Markets, LLC, Stifel, Nicolaus & Company, Incorporated and Truist Securities, Inc. and dated as of April 24, 2026, with each of Cantor Fitzgerald & Co. and Huntington Securities, Inc. (each, in its capacity as agent and/or principal, and together with any other such agent and/or principal with which the Company enters into an Alternative Distribution Agreement, an “Alternative Manager”), for the issuance and sale of the Securities from time to time through the applicable Alternative Managers on the terms set forth in the applicable Alternative Distribution Agreements. The aggregate offering price of the Securities that may be sold pursuant to this Agreement and the Alternative Distribution Agreements shall not exceed the Maximum Amount.¹

2.            Governing Law. THIS AMENDMENT AND ANY CLAIM, CONTROVERSY OR DISPUTE ARISING UNDER OR RELATED TO THIS AMENDMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK WITHOUT REGARD TO ITS CHOICE OF LAW PROVISIONS. SPECIFIED TIMES OF DAY REFER TO NEW YORK CITY TIME.

¹ Remove the agent signing applicable EDA amendment. 

3.             Counterparts. This Amendment may be executed in any number of counterparts, each of which shall be deemed to be an original, but all such counterparts shall together constitute one and the same agreement. Counterparts may be delivered via facsimile, electronic mail (including any electronic signature covered by the U.S. federal ESIGN Act of 2000, Uniform Electronic Transactions Act, the New York Electronic Signatures and Records Act or other applicable law, e.g., www.docusign.com) or other transmission method and any counterpart so delivered shall be deemed to have been duly and validly delivered and be valid and effective for all purposes.

4.              Agreement Remains in Effect. Except as provided in this Amendment, all provisions, terms and conditions of the Agreement shall remain in full force and effect. As amended hereby, the Agreement is ratified and confirmed in all respects.

[Signature Page Follows]

If the foregoing is in accordance with your understanding of our agreement, please sign and return to the Company a counterpart hereof, whereupon this instrument, along with all counterparts, will become a binding agreement among the Manager, the Operating Partnership, the Adviser and the Company in accordance with its terms.

Signature Page to Amendment No. 1 to the Equity Distribution Agreement

The foregoing Amendment No. 1 to the Agreement is hereby confirmed and accepted as of the date first written above.

Signature Page to Amendment No. 1 to the Equity Distribution Agreement