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Inspired by precision tests of the Standard Model in future lepton colliders,the numerical analysis of the following scattering processes, $e^+e^-\rightarrow Z h^0\gamma$ and $e^+e^- \rightarrow Z H^0 \gamma$, are carried atthe tree level including all possible diagrams in the two-Higgs-doublet model(2HDM). This model has many free parameters, but the parameters which take partin the scattering amplitudes of these two processes are primarily the mixingangle parameter, $s_{\beta-\alpha}$, and the masses of the neutral Higgsbosons, ($h^0, H^0$). Therefore, measuring the production rates of $Zh^0\gamma$ and $Z H^0 \gamma$ final states open another test for the scalarsectors of the 2HDM. The numerical analysis is performed under the currentexperimental constraints. The production rates and the asymmetry in theforward-backward direction are presented as a function of the center-of-massenergy covering the future lepton colliders. The unpolarized cross-section getsup to 6.19 (4.86) fb at $\sqrt{s} = 350$ (500) GeV and 0.164 (0.157) fb at$\sqrt{s} = 350$ (500) GeV for $e^+e^- \rightarrow Z h^0\gamma$ and $e^+e^-\rightarrow Z H^0 \gamma$, respectively. The polarization of the incoming$e^+e^-$ beams are studied for various configurations, and it enhances thecross-section by a factor of 1.78 in both processes for$P_{e^+,e^-}=(+0.6,-0.8)$.

Production of neutral Higgs bosons associated with Z-boson and photon in 2HDM at future lepton colliders