First measurements of the branching fractions of $J\mathrm{/}\psi \to {\mathrm{\Xi }}^0\bar{\mathrm{\Lambda }}{K}_S^0+c\mathrm{.}c\mathrm{.}$, $J\mathrm{/}\psi \to {\mathrm{\Xi }}^0{\bar{\mathrm{\Sigma }}}^0{K}_S^0+c\mathrm{.}c\mathrm{.}$, and $J\mathrm{/}\psi \to {\mathrm{\Xi }}^0{\bar{\mathrm{\Sigma }}}^{-}{K}^{+}+c\mathrm{.}c\mathrm{.}$

By analyzing $(10087\pm 44)\times {10}^6$ $J\mathrm{/}\psi$ events collected with the BESIII detector at the BEPCII, the decays $J\mathrm{/}\psi \to {\mathrm{\Xi }}^0\bar{\mathrm{\Lambda }}{K}_S^0+c\mathrm{.}c\mathrm{.}$, $J\mathrm{/}\psi \to {\mathrm{\Xi }}^0{\bar{\mathrm{\Sigma }}}^0{K}_S^0+c\mathrm{.}c\mathrm{.}$, and $J\mathrm{/}\psi \to {\mathrm{\Xi }}^0{\bar{\mathrm{\Sigma }}}^{-}{K}^{+}+c\mathrm{.}c\mathrm{.}$ are observed for the first time. Their branching fractions are determined to be $\mathcal{B}(J\mathrm{/}\psi \to {\mathrm{\Xi }}^0\bar{\mathrm{\Lambda }}{K}_S^0+c\mathrm{.}c\mathrm{.})=(3.76\pm 0.14\pm 0.23)\times {10}^{-5}$, $\mathcal{B}(J\mathrm{/}\psi \to {\mathrm{\Xi }}^0{\bar{\mathrm{\Sigma }}}^0{K}_S^0+c\mathrm{.}c\mathrm{.})=(2.24\pm 0.32\pm 0.31)\times {10}^{-5}$, and $\mathcal{B}(J\mathrm{/}\psi \to {\mathrm{\Xi }}^0{\bar{\mathrm{\Sigma }}}^{-}{K}^{+}+c\mathrm{.}c\mathrm{.})=(5.64\pm 0.17\pm 0.28)\times {10}^{-5}$, where the first uncertainties are statistical and the second systematic.