Some extended models predict the existence of a new neutral massive gauge boson, identified as the $Z^\prime$ boson, together with flavor-changing neutral currents. In this theoretical framework, we estimate the intensity of couplings regarding the interaction between the $Z'$ boson with the bottom and the strange quarks through the $B^0_s\to\mu^{+}{\mu^{-}}$ transition, which allow us to study the $B^0_s\to \tau \mu, \tau e, \mu e$ decays. We present preliminary results, where the corresponding branching ratios are estimated; our predictions are contrasted with similar ones coming from several extended models. In particular, our estimates for the branching ratios range between $10^{-9}$ and $10^{-6}$.