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One-loop form factors for $h\rightarrow e^-e^+\gamma$ and $e^-e^+\rightarrowh\gamma$ in $U(1)_{B-L}$ extension of the standard model are presented in thiswork. The computations are performed in 't Hooft-Veltman gauge. Analyticalresults are then expressed in terms of Passarino-Veltman functions followingthe standard notations of {\tt LoopTools}. As a results, one-loop form factorscan be evaluated numerically by using {\tt LoopTools}. In phenomenologicalresults, the signal strengths of $e^-e^+\rightarrow h\gamma$, defined as ratioof cross sections computed in $U(1)_{B-L}$ extension models to thecorresponding ones in the standard model, are analyzed at future leptoncolliders. The signal strengths for both vector and chiral $B-L$ models arescanned in physical parameter space. We find that the effects of charged Higgsin the chiral $B-L$ model can be probed easily with the help of the initialpolarization beams at future lepton colliders.

One-loop form factors for $h\rightarrow e^-e^+\gamma$ and $e^-e^+\rightarrow h\gamma$ in $U(1)_{B-L}$ extension of the standard model