We study associated Higgs production with a photon at electron-positron colliders, $e^+e^-to hgamma$, in various extended Higgs models, such as the inert doublet model (IDM), the inert triplet model (ITM) and the two Higgs doublet model (THDM). The cross section in the standard model (SM) is maximal around $sqrt{s}=$250 GeV, and we present how and how much the new physics can enhance or reduce the production rate. We also discuss the correlation with the $htogammagamma$ and $hto Zgamma$ decay rates. We find that, with a sizable coupling to a SM-like Higgs boson, charged scalars can give considerable contributions to both the production and the decay if their masses are around 100 GeV. Under the theoretical constraints from vacuum stability and perturbative unitarity as well as the current constraints from the Higgs measurements at the LHC, the production rate can be enhanced from the SM prediction at most by a factor of two in the IDM. In the ITM, in addition, we find a particular parameter region where the $hgamma$ production significantly increases by a factor of about six to eight, but the $htogammagamma$ decay still remains as in the SM. In the THDM, possible deviations from the SM prediction are minor in the viable parameter space.
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