Measurement of the inclusive branching fraction for

Using 5.9 pb$^{−1}$ of ${e}^{+}{e}^{-}$ annihilation data collected at center-of-mass energies from 3.640 to 3.701 GeV with the BESIII detector at the BEPCII Collider, we measure the observed cross sections of ${e}^{+}{e}^{-}\to {K}_{S}^{0}X$ (where $X=\text{anything}$). From a fit to these observed cross sections with the sum of continuum and $\psi \left(3686\right)$ and $J/\psi $ Breit-Wigner functions and considering initial state radiation and the BEPCII beam energy spread, we obtain for the first time the product of $\psi \left(3686\right)$ leptonic width and inclusive decay branching fraction ${\Gamma }_{\psi \left(3686\right)}^{ee}B\left(\psi \left(3686\right)\to {K}_{S}^{0}X\right)=\left(373.8±6.7±20.0\right)$ eV, and assuming ${\Gamma }_{\psi \left(3686\right)}^{ee}$ is $\left(2.33±0.04\right)$ keV from PDG value, we measure $B\left(\psi \left(3686\right)\to {K}_{S}^{0}X\right)=\left(16.04±0.29±0.90\right)\text{%}$, where the first uncertainty is statistical and the second is systematic.