Exhibit 23.1

Independent Registered Public Accounting Firm’s Consent

We consent to the inclusion in this Registration Statement of Alpha Healthcare Acquisition Corp. III (the “Company”) on Form S-1 of our report dated February 1, 2021, except for the second paragraph of Note 8 as to which the date is March 4, 2021, which includes an explanatory paragraph as to the Company’s ability to continue as a going concern, with respect to our audit of the financial statements of Alpha Healthcare Acquisition Corp. III as of January 25, 2021 and for the period from January 21, 2021 (inception) through January 25, 2021, which report appears in the Prospectus, which is part of this Registration Statement. We also consent to the reference to our Firm under the heading “Experts” in such Prospectus.

/s/ Marcum llp

Marcum llp

New York, NY

March 4, 2021