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 $bar B^0_sto ,pi^0,eta$ 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 $B^0_sto,rho^0,eta$ 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 $S_{psiphi}$ 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 $S_{Z} (B_s) simeq -2 S_{SM} (B_s)$.
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