We calculate bounds for the branching ratio of the B0s→τe decay, for the first time, in the context of flavor changing neutral currents mediated by a Z′ gauge boson, which can arise from five extended models. In this sense, by using experimental measurements on the B→Xsγ decay and the B0s→μ+μ− process, we look for constraints of the Z′bs coupling, where the more restrictive bound is offered by the last one. On the other hand, by employing the experimental restriction on the τ→eeē decay, the strength of the Z′τe coupling is estimated. Our analysis is based on the more recent experimental results on searches for the Z′ gauge boson in ATLAS and CMS detectors. In addition, we revisited the B0s→τμ,μe meson decays by using different approaches not previously reported. The strengths of the Z′τμ and Z′μe couplings were estimated by employing experimental restrictions on the τ→μμˉμ decay and the μ−e conversion rate, respectively. Thus, we predict the following upper bounds: B0s→τe∼10−6, B0s→τμ∼10−6 and B0s→μe∼10−11.