  To shed light on the indirect search for new physics beyond the standard
model, the long standing discrepancies between the theory and experiment
mediated by FCNC $b\to s \ell \ell$ quark level transitions set an ideal
testing ground. Though the very recent measurements of $R_K$ and $R_{K^*}$ are
consistent with the standard model, still the excitements remain on the
measurements of LHCb experiment with the observables $\mathcal{B} (B_s \to \phi
\mu ^+ \mu ^-)$ which has deviations at the level of $3.6 \sigma$.
Additionally, standard deviation of $\sim 3.3 \sigma$ and $1.2 \sigma$,
respectively for $P_5^{\prime}$ in $B \to K^* \mu ^+ \mu ^-$ and the branching
ratio in $B_s \to \mu^+ \mu^-$ processes are observed. Inspired by these
discrepancies, we work out the constraints on the new physics coupling
parameters in the presence of a non-universal $Z'$ model. We then probe the
exclusive leptonic decay channels $ B_s \to \ell \ell^{\prime}$, $B_{(s)} \to
(K^{(*)}, \phi, f_2^{\prime}, K_2^*) \ell \ell ^{\prime}$ induced by the
neutral current transition $b\to s \ell \ell^{\prime}$. We find that the $q^2$
variation of the observables, such as, branching ratio, forward-backward
asymmetry, lepton polarization asymmetry, and the very sensible observable, so
called non-universality observables for LFV decays display the sensitivity of
new physics. In this analysis. we estimate above mentioned observables that
could shed light on the window of new physics in the near future.
