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The recent experimental results including $R_{K^{(\ast)}}$, $R_{D^{(\ast)}}$,$(g-2)_\mu$ and $W$ mass show deviations from the standard model (SM)predictions, implying the clues of new physics (NP). In this work, weinvestigate the explanations of these anomalies in the $R$-parity violatingminimal supersymmetric standard model (RPV-MSSM) extended with the inverseseesaw mechanism. The non-unitarity extent $\eta_{ee}$ and the loop correctionsfrom the interaction $\lambda'\hat L \hat Q \hat D$ are utilized to raise theprediction of $W$ mass through muon decays. We also find that the interaction$\lambda'\hat L \hat Q \hat D$ involved with right-handed (RH)/singlet(s)neutrinos can explain the $R_{K^{(\ast)}}$ and $R_{D^{(\ast)}}$ anomaliessimultaneously when considering nonzero $\lambda'_{1jk}$. For nonzero$\lambda'_{2jk}$, this model fulfills the whole $b\to s\ell^+\ell^-$ fit butcannot be accordant with $R_{D^{(\ast)}}$ measurements. The explanations inboth cases are also favored by $(g-2)_\mu$ data, neutrino oscillation data andthe relevant constraints we scrutinized. Furthermore, this model framework canbe tested in future experiments covering, e.g., the predicted lepton flavorviolations (LFV) at Belle II and the Future Circular Collider with $e^+e^-$beams (FCC-ee), as well as the heavy neutrinos at future colliders.

Explaining anomalies of $B$-physics, muon $g-2$ and $W$ mass in $R$-parity violating MSSM with seesaw mechanism