A complete one-loop prediction for the single production of the neutral Higgs bosons in association with a photon in electron-positron collisions is presented in the framework MSSM, paying special attention to the individual contribution from each type of diagram. This process has no amplitude at tree level and is hence directly sensitive to one-loop impacts and the underlying dynamics of Higgs. In order to investigate the effect of the new physics, four different scenarios, which include a Higgs boson with mass and couplings consistent with those of the discovered Higgs boson and a considerable part of parameter space allowed by the bounds from the researches for additional Higgs bosons and sparticles, are chosen in the MSSM. The dependence of the cross section in both SM and MSSM on the center-of-mass energy is examined by considering the polarizations of the initial electron and positron beams. The effect of individual contributions from each type of oneloop diagrams on the total cross section is also investigated in detail. Furthermore, the total cross section of e − e + → γh 0 as well as e − e + → γA 0 are scanned over the plane mA − tan β for each scenario. The full one-loop contributions are crucial for the analysis of BSM physics at a future electron-positron collider. 12.60.Jv, 13.66.Fg, 14.80.Da * The diagrams were drawn by using JaxoDraw [32,33].