We perform an analysis of the consequences of various new physics operators on the lepton flavor violating (LFV) decay modes mediated through $b\to s{\ell }_1{\ell }_2$ transitions. We scrutinize the imprints of the (pseudo)scalar and axial (vector) operators on the exclusive LFV decay channels $B_{\left(s\right)}\to (\varphi ,K^{⁎},K_2^{⁎}){\ell }_1{\ell }_2$ and ${\Lambda }_b\to \Lambda {\ell }_1{\ell }_2$, where ${\ell }_1,{\ell }_2$ represent μ or τ. The new physics parameters are constrained by using the upper limits of the branching fractions of the $B_s\to \tau \mu$ and $B\to K\tau \mu$ processes, assuming the new physics couplings to be real. We then explore the key observables such as the branching fractions, the forward-backward asymmetries, and the longitudinal polarization fractions of the $B\to (K^{⁎},\varphi ,K_2^{⁎}){\tau }^{\pm }{\mu }^{\mp }$ decays. In addition, we also investigate the impact of the new physics couplings on the baryonic ${\Lambda }_b\to \Lambda {\tau }^{\pm }{\mu }^{\mp }$ decay channels mediated by the $b\to s$ quark level transition. With the experimental prospects at LHCb upgrade and Belle II, we also predict the upper limits of the above-discussed observables, which could intrigue the new physics search in these channels.