  We scrutinize the penguin dominated $ B_s \to K^+ K^-$ decay mode involving
$b \to s$ quark level transition in family non-universal $Z^ \prime$ and
vector-like down quark model. There is discrepancy in the standard model
branching ratio value of this mode with the experimental results reported by
Belle, CDF and LHCb Collaborations. Additionally, the measured values of
CP-violating asymmetries $ C_{K^+K^-}$ and $ S_{K^+K^-}$ deviate from the SM
results. We constrain the new parameter space by using the existing
experimental limits on leptonic $ B_s\to \ell \ell$ ($\ell = e, \mu, \tau$)
processes. We then check the effects of new physics on the branching ratio and
CP violating parameters of the $ B_s \to K^+ K^-$ process.
