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Motivated by recent $R_D$, $R_{D^*}$ and $R_{J/\psi}$ anomalies in $B\toD\ell^- \bar{\nu}_{\ell}$, $B\to D^*\ell^- \bar{\nu}_{\ell}$ and $B_c\toJ/\psi\ell^- \bar{\nu}_{\ell}$ decays, respectively, we study possible R-parityviolating supersymmetric effects in $B_c\to J/\psi\ell^-\bar{\nu}_{\ell},\eta_c\ell^- \bar{\nu}_{\ell}$ and $\Lambda_b \to \Lambda_c\ell^- \bar{\nu}_{\ell}$ decays, which are also induced by $b\to c \ell^-\bar{\nu}_{\ell}$ at quark level. We find that (I) the constrained sleptonexchange couplings $\lambda_{i33}\tilde{\lambda}'^*_{i23}$ involving in $b\to c\tau^- \bar{\nu}_{\tau}$ transition from relevant latest experimental datastill have quite large effects on all (differential) branching ratios and thenormalized forward-backward asymmetries of the exclusive semileptonic $b\to c\tau^- \bar{\nu}_{\tau}$ decays as well as the ratios of the (differential)branching ratios; (II) after satisfying the data of $R_D$ and $R_{D^*}$, theupper limit of $R_{J/\psi}$, $R_{\eta_c}$ and $R_{\Lambda_c}$ could beincreased by 10%, 112% and 24%, respectively, from their upper limits of theStandard Model predictions by the $\lambda_{i33}\tilde{\lambda}'^*_{i23}$couplings. The results in this work could be used to probe R-parity violatingeffects and will correlate with searches for direct supersymmetric signals atthe running LHCb and the forthcoming Belle-II.

Probing the R-parity violating supersymmetric effects in $B_c\to  J/\psi\ell^-\bar{\nu}_{\ell},\eta_c\ell^-\bar{\nu}_{\ell}$ and  $\Lambda_b\to\Lambda_c\ell^-\bar{\nu}_{\ell}$ decays