$B_s^0\to {\mu }^{+}{\mu }^{-}$ in a flavor violating extension of MSSM

$B$ meson rare decays play a crucial role in exploring new physics beyond the standard model. In this study, we explore the rare decay process $B_s^0\to {\mu }^{+}{\mu }^{-}$ in a flavor violating extension of the Minimal Supersymmetric Standard Model (MSSM), namely the $\mu$-from-$\nu$ SSM ($\mu \nu$SSM). Combined with the decay $\bar{B}\to X_s\gamma$, the numerical results indicate that the $\mu \nu$SSM can successfully accommodate the experimental data for $B_s^0\to {\mu }^{+}{\mu }^{-}$ and additionally narrow down the parameter space.