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The decay modes $\bar{B}_s \rightarrow \pi^0(\rho^0 )\,\eta^{(')} $ aredominated by electroweak penguins that are small in the standard model. In thiswork we investigate the contributions to these penguins from a model with anadditional $U(1)'$ gauge symmetry and show there effects on the branchingratios of $\bar{B}_s \rightarrow \pi^0(\rho^0 )\,\eta^{(')} $. In a scenario ofthe model, where $Z^\prime$ couplings to the left-handed quarks vanish, we showthat the maximum enhancement occurs in the branching ratio of $\bar B^0_s\to\,\pi^0\,\eta'$ where it can reach $6$ times the SM prediction. On the otherhand, in a scenario of the model where $Z^\prime$ couplings to both left-handedand right-handed quarks do not vanish, we find that $Z^\prime$ contributionscan enhance the branching ratio of $B^0_s\to\,\rho^0\,\eta$ up to one order ofmagnitude comparing to the SM prediction for several sets of the parameterspace where both $ \Delta M_{B_s}$ and $S_{\psi\phi}$ constraints aresatisfied. This kind of enhancement occurs for a rather fine-tuned point where$ \Delta M_{B_s}$ constraint on $\mid S_{SM} (B_s) + S_{Z'} (B_s)\mid $ isfulfilled by overcompensating the SM via $S_{Z'} (B_s) \simeq -2 S_{SM} (B_s)$.

New physics contributions to $\bar{B}_s \rightarrow \pi^0(\rho^0 )\,\eta^{(')} $ decays