  We elucidate the recently observed discrepancy in the branching ratio of
$B^{+}\rightarrow K^{+}$ +inv decay mode using a GeV scale scalar dark matter
in an anomaly-free $U(1)_{B-L}$ gauge extension of the Standard Model. We
constrain the new parameters by using consistency with the existing bounds on
Dark matter relic density, direct detection, collider and BR($B\rightarrow
K^*\nu\bar{\nu}$) measured at the Belle II experiment. We investigate couplings
between the mediator and the SM fermions as well as the dark matter particle.
We then estimate the branching ratios of $b \to s \nu \bar \nu$ decay processes
such as $B\rightarrow (K^+,K^*)\nu\bar{\nu}$, $B_s\rightarrow
(\eta,\eta')\nu\bar{\nu}$, $ B_s\rightarrow \phi\nu\bar{\nu}$ and
$B_c\rightarrow (D_s, D_s^*)\nu\bar{\nu}$ in a common parameter space, meeting
the current experimental bounds of both sectors simultaneously.
