We study the $e^{+}{e}^{-}\to K^{+}(D_s^{⁎-}{D}^0+D_s^{-}{D}^{⁎0})$ reaction recently measured at BESIII, from where a new $Z_{cs}$ state has been reported. We study the interaction of ${\overline{D}}_s{D}^{⁎}$ with the coupled channels $J/\psi K^{-}$, $K^{⁎-}{\eta }_c$, $D_s^{-}{D}^{⁎0}$, $D_s^{⁎-}{D}^0$ by means of an extension to the charm sector of the local hidden gauge approach. We find that the $D_s^{-}{D}^{⁎0}+D_s^{⁎-}{D}^0$ combination couples to $J/\psi K^{-}$ and $K^{⁎-}{\eta }_c$, but the $D_s^{-}{D}^{⁎0}-D_s^{⁎-}{D}^0$ combination does not. The coupled channels help to build up strength in the $D_s^{-}{D}^{⁎0}+D_s^{⁎-}{D}^0$ diagonal scattering matrix close to threshold and, although the interaction is not strong enough to produce a bound state or resonance, it is sufficient to produce a large accumulation of strength at the ${\overline{D}}_s{D}^{⁎}$ threshold in the $e^{+}{e}^{-}\to K^{+}(D_s^{⁎-}{D}^0+D_s^{-}{D}^{⁎0})$ reaction in agreement with experiment.