We study the Higgs boson decays $$h \rightarrow Z\gamma $$ and $$h \rightarrow m_VZ$$ in a model with vectorlike fermions and $$U(1)_X$$ symmetry ( $$U(1)_X$$ VLFM), where $$m_V$$ is a vector meson ( $$\rho ,\ \omega ,\ \phi ,\ J/\psi ,\ \Upsilon $$ ). The exotic Yukawa interactions in this model generate mixing between Standard Model (SM) fermions and vectorlike fermions, and this mixing affects the Higgs boson mass and Higgs couplings. The corrections to the CP-even and CP-odd $$h\gamma Z$$ couplings come from loop diagrams that involve the new particles, and these corrections have a clear impact on the decay rates of $$h\rightarrow Z\gamma $$ and $$h\rightarrow m_VZ$$ . In suitable regions of the parameter space, the model can produce non-negligible deviations in $$\Gamma _\textrm{NP}(h\rightarrow Z\gamma )/\Gamma _\textrm{SM}(h\rightarrow Z\gamma )$$ and $$\Gamma _\textrm{NP}(h\rightarrow m_VZ)/\Gamma _\textrm{SM}(h\rightarrow m_V Z)$$ , providing possible signals of new physics (NP) beyond the SM.