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Abstract The lepton flavor universality violating (LFUV) measurements $$R_K$$ RK and $$R_{K^*}$$ RK∗ in B meson decays can be accounted for in non-universal $$Z'$$ Z′ models. We constrain the couplings of these $$Z'$$ Z′ models by performing a global fit to correlated $$b \rightarrow s \ell \ell $$ b→sℓℓ and $$b \rightarrow d \ell \ell $$ b→dℓℓ processes, and calculate their possible implications for $$B_s \rightarrow {\bar{K}}^*\ell \ell $$ Bs→K¯∗ℓℓ observables. For real new physics (NP) couplings, the 1$$\sigma $$ σ favored parameters allow the corresponding LFUV ratio $$R_{K^*}^{(s)}$$ RK∗(s) in $$B_s \rightarrow {\bar{K}}^*\ell \ell $$ Bs→K¯∗ℓℓ to range between 0.8 and 1.2 at low $$q^2$$ q2 . Complex NP couplings improve the best fit only marginally, however they allow a significant enhancement of the branching ratio, while increasing the range of $$R_{K^*}^{(s)}\ $$ RK∗(s) at low $$q^2$$ q2 to 0.8–1.8. We find that NP could cause zero-crossing in the forward–backward asymmetry $$A_{FB}$$ AFB to shift towards lower $$q^2$$ q2 values, and enhancement in the magnitude of integrated $$A_{FB}$$ AFB . The CP asymmetry $$A_{CP}$$ ACP may be suppressed and even change sign. The simultaneous measurements of integrated $$R_{K^*}^{(s)}\ $$ RK∗(s) and $$A_{CP}$$ ACP values to 0.1 and 1% respectively, would help in constraining the effective NP Wilson coefficient $$C_9$$ C9 in $$ b \rightarrow d \mu \mu $$ b→dμμ interactions.