[en] Motivated by recent $R_D$, $R_{D^{⁎}}$ and $R_{J/\psi }$ anomalies in $B\to D{\ell }^{-}{\overline{\nu }}_{\ell }$, $B\to D^{⁎}{\ell }^{-}{\overline{\nu }}_{\ell }$ and $B_c\to J/\psi {\ell }^{-}{\overline{\nu }}_{\ell }$ decays, respectively, we study possible R-parity violating supersymmetric effects in $B_c\to J/\psi {\ell }^{-}{\overline{\nu }}_{\ell },{\eta }_c{\ell }^{-}{\overline{\nu }}_{\ell }$ and ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c{\ell }^{-}{\overline{\nu }}_{\ell }$ decays, which are also induced by $b\to c{\ell }^{-}{\overline{\nu }}_{\ell }$ at quark level. We find that (I) the constrained slepton exchange couplings ${\lambda }_{i33}{\tilde{\lambda }}_{i23}^{\prime ⁎}$ involving in $b\to c{\tau }^{-}{\overline{\nu }}_{\tau }$ transition from relevant latest experimental data still have quite large effects on all (differential) branching ratios and the normalized forward–backward asymmetries of the exclusive semileptonic $b\to c{\tau }^{-}{\overline{\nu }}_{\tau }$ decays as well as the ratios of the (differential) branching ratios; (II) after satisfying the data of $R_D$ and $R_{D^{⁎}}$, the upper limit of $R_{J/\psi }$, $R_{{\eta }_c}$ and $R_{{\mathrm{\Lambda }}_c}$ could be increased by 10%, 112% and 24%, respectively, from their upper limits of the Standard Model predictions by the ${\lambda }_{i33}{{\tilde{\lambda }}^{\prime ⁎}}_{i23}$ couplings. The results in this work could be used to probe R-parity violating effects and will correlate with searches for direct supersymmetric signals at the running LHCb and the forthcoming Belle-II.