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Abstract The decays of top quark $$t\rightarrow c\gamma ,\;t\rightarrow cg,\;t\rightarrow cZ,\;t\rightarrow ch$$ t→cγ,t→cg,t→cZ,t→ch are extremely rare processes in the standard model (SM). The predictions on the corresponding branching ratios in the SM are too small to be detected in the future, hence any measurable signal for the processes at the LHC is a smoking gun for new physics. In the extension of minimal supersymmetric standard model with an additional local $$U(1)_B\text {--}L$$ U(1)B--L gauge symmetry (B-LSSM), new gauge interaction and new flavor changing interaction affect the theoretical evaluations on corresponding branching ratios of those processes. In this work, we analyze those processes in the B-LSSM, under a minimal flavor violating assumption for the soft breaking terms. Considering the constraints from updated experimental data, the numerical results imply $$Br(t\rightarrow c\gamma )\sim 5\times 10^{-7}$$ Br(t→cγ)∼5×10-7 , $$Br(t\rightarrow cg)\sim 2\times 10^{-6}$$ Br(t→cg)∼2×10-6 , $$Br(t\rightarrow cZ)\sim 4\times 10^{-7}$$ Br(t→cZ)∼4×10-7 and $$Br(t\rightarrow ch)\sim 3\times 10^{-9}$$ Br(t→ch)∼3×10-9 in our chosen parameter space. Simultaneously, new gauge coupling constants $$g_{_B},\;g_{_{YB}}$$ gB,gYB in the B-LSSM can also affect the numerical results of $$Br(t\rightarrow c\gamma ,\;cg,\;cZ,\;ch)$$ Br(t→cγ,cg,cZ,ch) .