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To shed light on the indirect search for new physics beyond the standardmodel, the long standing discrepancies between the theory and experimentmediated by FCNC $b\to s \ell \ell$ quark level transitions set an idealtesting ground. Though the very recent measurements of $R_K$ and $R_{K^*}$ areconsistent with the standard model, still the excitements remain on themeasurements 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 branchingratio in $B_s \to \mu^+ \mu^-$ processes are observed. Inspired by thesediscrepancies, we work out the constraints on the new physics couplingparameters in the presence of a non-universal $Z'$ model. We then probe theexclusive leptonic decay channels $ B_s \to \ell \ell^{\prime}$, $B_{(s)} \to(K^{(*)}, \phi, f_2^{\prime}, K_2^*) \ell \ell ^{\prime}$ induced by theneutral current transition $b\to s \ell \ell^{\prime}$. We find that the $q^2$variation of the observables, such as, branching ratio, forward-backwardasymmetry, lepton polarization asymmetry, and the very sensible observable, socalled non-universality observables for LFV decays display the sensitivity ofnew physics. In this analysis. we estimate above mentioned observables thatcould shed light on the window of new physics in the near future.

Delving into the $ B_s \to \ell \ell^{\prime}$, $B_{(s)} \to (K^{(*)}, \phi, f_2^{\prime}, K_2^*) \ell \ell ^{\prime}$ processes

Delving into the $ B_s \to \ell \ell^{\prime}$, $B_{(s)} \to (K^{()}, \phi, f_2^{\prime}, K_2^) \ell \ell ^{\prime}$ processes