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We present the cross section for $e^{+}e^{-}\to hZ$ with arbitrary sets ofelectron and $Z$ boson polarizations at the full next-to-leading order invarious extended Higgs models, such as the Higgs singlet model (HSM), the inertdoublet model (IDM) and the two Higgs doublet model (2HDM). We systematicallyperform complete one-loop calculations to the helicity amplitudes in theon-shell renormalization scheme, and present the full analytic results as wellas numerical evaluations. The deviation $\Delta R^{hZ}$ in the total crosssection from its standard model (SM) prediction is comprehensively analyzed,and the differences among these models are discussed in details. We find thatnew physics effects appearing in the renormalized $hZZ$ vertex almost governthe behavior of $\Delta R^{hZ}$, and it takes a negative value in most cases.The possible size of $\Delta R^{hZ}$ reaches several percent under thetheoretical and experimental bounds. We also analyze the deviation $\DeltaR^{hZ}_{XY}$ in the total cross section times decay branching ratios of thediscovered Higgs boson by utilizing the $\texttt{H-COUP}$ program. It is foundthat the four types of 2HDMs can be discriminated by analyzing the correlationbetween $\Delta R^{hZ}_{\tau\tau}$ and $\Delta R^{hZ}_{bb}$ and those between$\Delta R^{hZ}_{\tau\tau}$ and $\Delta R^{hZ}_{cc}$. Furthermore, the HSM andthe IDM can be discriminated from the 2HDMs by measuring $\Delta R^{hZ}_{WW}$.These signatures can be tested by precision measurements at future Higgsfactories such as the International Linear Collider.

Next-to-leading-order corrections to the Higgs strahlung process from electron-positron collisions in extended Higgs models