Lepton-number violation can be induced by the exchange of an on-shell Majorana neutrino $N$ in semileptonic $|\mathrm{\ensuremath{\Delta}}L|=2$ decays of the ${B}_{s}$ meson, ${B}_{s}^{0}\ensuremath{\rightarrow}{P}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{+}$ with $P=K,{D}_{s}$. We investigate the production of such a heavy sterile neutrino through these four-body ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{+}$ channels and explore the sensitivity that can be reached at the LHCb and CMS experiments. For heavy neutrino lifetimes of ${\ensuremath{\tau}}_{N}=[1,100,1000]\text{ }\text{ }\mathrm{ps}$ and integrated luminosities collected of 10 and $50\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at the LHCb and 30, 300, and $3000\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at the CMS, we find a significant sensitivity on branching fractions of the orders $\mathrm{BR}({B}_{s}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{+})\ensuremath{\lesssim}\mathcal{O}({10}^{\ensuremath{-}9}--{10}^{\ensuremath{-}8})$ and $\mathrm{BR}({B}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{\ensuremath{-}}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{+})\ensuremath{\lesssim}\mathcal{O}({10}^{\ensuremath{-}8}--{10}^{\ensuremath{-}7})$. In the kinematically allowed mass ranges of ${m}_{N}\ensuremath{\in}[0.25,4.77]\text{ }\text{ }\mathrm{GeV}$ and ${m}_{N}\ensuremath{\in}[0.25,3.29]\text{ }\text{ }\mathrm{GeV}$, respectively, we exclude regions on the parameter space $({m}_{N},|{V}_{\ensuremath{\mu}N}{|}^{2})$ associated with the heavy neutrino, which could slightly improve the limits from ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}{\ensuremath{\mu}}^{\ensuremath{-}}$ (LHCb).