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Focusing on the leptonic channels $B \\to \\mu N$ and $B \\to \\tau N$, we constrain the allowed regions in the $M_N$--$|U_{\\ell N}|^2$ plane using current experimental data. Using these constraints, we investigate lepton-number violating ($\\Delta L=2$) processes mediated by on-shell HNLs, including $B_{(c)}^- \\to \\pi^+ \\mu^- \\mu^-$ and $B_c^- \\to J/\\psi\\, \\pi^+ \\mu^- \\mu^-$. 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Focusing on the leptonic channels $B \\to \\mu N$ and $B \\to \\tau N$, we constrain the allowed regions in the $M_N$--$|U_{\\ell N}|^2$ plane using current experimental data. Using these constraints, we investigate lepton-number violating ($\\Delta L=2$) processes mediated by on-shell HNLs, including $B_{(c)}^- \\to \\pi^+ \\mu^- \\mu^-$ and $B_c^- \\to J/\\psi\\, \\pi^+ \\mu^- \\mu^-$. For benchmark values $|U_{\\mu N}|^2 = 10^{-6}$ and $M_N = 2$-- $3\\,\\mathrm{GeV}$, the predicted br"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For benchmark values |U_μN|^2 = 10^{-6} and M_N = 2--3 GeV, the predicted branching ratios lie in the range O(10^{-13})--O(10^{-8}). 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