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We present a detailed analysis of the Higgs boson decays $h\rightarrow Z\gamma$ and $h\rightarrow m_V Z$ in the $U(1)_X$SSM, with $m_V$ denoting themeson ($\omega,\rho,\phi,J/{\psi},\Upsilon$). Using the effective Lagrangianmethod, we calculate the effective constants $C_{\gamma Z}$ (CP-even) and$\tilde{C}_{\gamma Z}$ (CP-odd) for the vertex $h \gamma Z$, which arecorrected by the new particle loop diagrams. Numerically, the ratio${\Gamma}_{U(1)_X}(h\rightarrow Z \gamma )/{\Gamma}_{SM}(h\rightarrow Z\gamma)$ is between $1.02-1.35$. For the vector mesons $\omega,\rho,\phi$ and$J/{\psi}$, the ratios ${\Gamma}_{U(1)_X}(h\rightarrow m_V Z)/{\Gamma}_{SM}(h\rightarrow m_V Z)$ are mainly distributed in the range of($1.01-1.45$). When $m_V$ represents $\Upsilon$, the larger value of the ratio${\Gamma}_{U(1)_X}(h\rightarrow \Upsilon Z )/{\Gamma}_{SM}(h\rightarrow\Upsilon Z)$ is mostly located in the range of ($1.002-1.30$). This work canprovide a reference for specific types of decay processes which can be searchedin LHC.

Higgs boson decays $h\rightarrow Z \gamma$ and $h\rightarrow m_V Z$ in the $U(1)_X$SSM