We investigate the one-loop prediction for the single production of a SM-like Higgs boson in association with a photon during electron-positron collisions within the framework of the two Higgs doublet type-II seesaw model (2HDMcT). In this study \(h_1\) is identified as the SM-like Higgs boson at 125 GeV. Our results indicate that the newly introduced charged scalars, namely \(H_1^\pm \) , \(H_2^\pm \) , and \(H^{\pm \pm }\) , have a noteworthy impact on both the rates of production and decays. Additionally our analysis shows that these observables are especially sensitive to the parameter \(\alpha _1\) . This influence produce a substantial contribution to both \(R_{\gamma \gamma }\) and \(\sigma (e^+e^- \to h_1\gamma )\) , and leads to \(R_{\gamma \gamma }\) that agrees with the observed signal strength within \(1\sigma \) confidence level (C.L) and to \(\sigma (e^+e^- \to h_1\gamma )\) that can reach and even exceed the Standard Model (SM) prediction up to \(8.06\,\times \, 10^{-2}\) fb.