  The decay modes $\bar{B}_s \rightarrow \pi^0(\rho^0 )\,\eta^{(')} $ are
dominated by electroweak penguins that are small in the standard model. In this
work we investigate the contributions to these penguins from a model with an
additional $U(1)'$ gauge symmetry and show there effects on the branching
ratios of $\bar{B}_s \rightarrow \pi^0(\rho^0 )\,\eta^{(')} $. In a scenario of
the model, where $Z^\prime$ couplings to the left-handed quarks vanish, we show
that 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 other
hand, in a scenario of the model where $Z^\prime$ couplings to both left-handed
and right-handed quarks do not vanish, we find that $Z^\prime$ contributions
can enhance the branching ratio of $B^0_s\to\,\rho^0\,\eta$ up to one order of
magnitude comparing to the SM prediction for several sets of the parameter
space where both $ \Delta M_{B_s}$ and $S_{\psi\phi}$ constraints are
satisfied. 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 $ is
fulfilled by overcompensating the SM via $S_{Z'} (B_s) \simeq -2 S_{SM} (B_s)$.
