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Using E1 radiative transitions $\ensuremath{\psi}(3686)\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\chi}}_{cJ}$ from a sample of $(448.1\ifmmode\pm\else\textpm\fi{}2.9)\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }\ensuremath{\psi}(3686)$ events collected with the BESIII detector, the decays ${\ensuremath{\chi}}_{cJ}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{+}\overline{p}{K}_{S}^{0}+\mathrm{c}.\mathrm{c}.(J=0,1,2)$ are studied. The decay branching fractions are measured to be $\mathcal{B}({\ensuremath{\chi}}_{c0}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{+}\overline{p}{K}_{S}^{0}+\mathrm{c}.\mathrm{c}.)=(3.52\ifmmode\pm\else\textpm\fi{}0.19\ifmmode\pm\else\textpm\fi{}0.21)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, $\mathcal{B}({\ensuremath{\chi}}_{c1}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{+}\overline{p}{K}_{S}^{0}+\mathrm{c}.\mathrm{c}.)=(1.53\ifmmode\pm\else\textpm\fi{}0.10\ifmmode\pm\else\textpm\fi{}0.08)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, and $\mathcal{B}({\ensuremath{\chi}}_{c2}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}^{+}\overline{p}{K}_{S}^{0}+\mathrm{c}.\mathrm{c}.)=(8.25\ifmmode\pm\else\textpm\fi{}0.83\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.49)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$, where the first and second uncertainties are the statistical and systematic ones, respectively. No evident …