Observation of a Near-Threshold Structure in the ${K}^{+}$ Recoil-Mass Spectra in ${e}^{+}{e}^{-}\to {K}^{+}\left({D}_{s}^{-}{D}^{*0}+{D}_{s}^{*-}{D}^{0}\right)$

We report a study of the processes of ${e}^{+}{e}^{-}\to {K}^{+}{D}_{s}^{-}{D}^{*0}$ and ${K}^{+}{D}_{s}^{*-}{D}^{0}$ based on ${e}^{+}{e}^{-}$ annihilation samples collected with the BESIII detector operating at BEPCII at five center-of-mass energies ranging from 4.628 to 4.698 GeV with a total integrated luminosity of $3.7\text{}\text{}{\mathrm{fb}}^{-1}$. An excess of events over the known contributions of the conventional charmed mesons is observed near the ${D}_{s}^{-}{D}^{*0}$ and ${D}_{s}^{*-}{D}^{0}$ mass thresholds in the ${K}^{+}$ recoil-mass spectrum for events collected at $\sqrt{s}=4.681\text{}\text{}\mathrm{GeV}$. The structure matches a mass-dependent-width Breit-Wigner line shape, whose pole mass and width are determined as $\left({3982.5}_{-2.6}^{+1.8}±2.1\right)\text{}\text{}\mathrm{MeV}/{c}^{2}$ and $\left({12.8}_{-4.4}^{+5.3}±3.0\right)\text{}\text{}\mathrm{MeV}$, respectively. The first uncertainties are statistical and the second are systematic. The significance of the resonance hypothesis is estimated to be $5.3\text{}\text{}\sigma $ over the contributions only from the conventional charmed mesons. This is the first candidate for a charged hidden-charm tetraquark with strangeness, decaying into ${D}_{s}^{-}{D}^{*0}$ and ${D}_{s}^{*-}{D}^{0}$. However, the properties of the excess need further exploration with more statistics.