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Abstract We study the one-loop prediction for the single production of a SM-like Higgs boson in association with a photon in electron-positron collisions in the context of the two Higgs doublet type-II seesaw model (2HDMcT). We explore to what extent the new scalars in the 2HDMcT spectrum affect its production cross-section, the ratio $$R_{\gamma h_1}$$ R γ h 1 as well as the signal strengths $$R_{\gamma Z}$$ R γ Z and $$R_{\gamma \gamma }$$ R γ γ when $$h_1$$ h 1 is identified with the observed SM Higgs boson within the 2HDMcT delimited parameter space. More specifically, we focus on $$e^+e^- \rightarrow h_1\gamma $$ e + e - → h 1 γ process at one-loop, and analyzed how it evolves under a full set of theoretical constraints and the available experimental data, including $$B\rightarrow X_s\gamma $$ B → X s γ limit at 95 $$\%$$ % C.L. Our analysis shows that these observables are strongly dependent on the parameters of the model, especially the mixing angel $$\alpha _1$$ α 1 , the potential parameters $$\lambda _{7}$$ λ 7 , $$\lambda _{9}$$ λ 9 , the trilinear Higgs couplings, with a noticeable sensitivity to $$\alpha _1$$ α 1 . We found that $$\sigma (e^+e^- \rightarrow h_1\gamma )$$ σ ( e + e - → h 1 γ ) can significantly be enhanced up to $$8.1\,\,\times 10^{-2}$$ 8.1 × 10 - 2 fb, thus exceeding the Standard Model prediction. Additionally, as a byproduct, we also observed that $$R_{\gamma h_1}$$ R γ h 1 is entirely correlated with both the $$h_1\rightarrow \gamma \gamma $$ h 1 → γ γ and $$h_1\rightarrow \gamma Z$$ h 1 → γ Z signal strengths.