In this paper, we present predictions for scattering cross section the of Higgs boson pair production via photon fusion at future muon colliders, focusing specifically the production processes μ+μ-→γγ→h0h0,A0A0. We investigated the impact of three choices the photon structure functions on cross-section predictions for a range model input parameters within the theoretical framework of the Higgs triplet model [Phys. Rev. D 84, 095005 (2011)PRVDAQ1550-799810.1103/PhysRevD.84.095005; Eur. Phys. J. C 79, 940 (2019)EPCFFB1434-604410.1140/epjc/s10052-019-7471-3; Phys. Rev. D 22, 2227 (1980)PRVDAQ0556-282110.1103/PhysRevD.22.2227; Phys. Rev. D 25, 2951 (1982)PRVDAQ0556-282110.1103/PhysRevD.25.2951]. © 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.