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We report a study of the processes of e+e−→K+(D−sD∗0+D∗−sD0) 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 fb−1. An excess over the known contributions of the conventional charmed mesons is observed near the D−sD∗0 and D∗−sD0 mass thresholds in the K+ recoil-mass spectrum for events collected at s√=4.681 GeV. The structure matches a mass-dependent-width Breit-Wigner line shape, whose pole mass and width are determined as (3982.5+1.8−2.6±2.1) MeV/c2 and (12.8+5.3−4.4±3.0) MeV, respectively. The first uncertainties are statistical and the second are systematic. The significance of the resonance hypothesis is estimated to be 5.3 σ over the pure contributions from the conventional charmed mesons. This is the first candidate of the charged hidden-charm tetraquark with strangeness, decaying into D−sD∗0 and D∗−sD0. However, the genuine properties of the excess need further exploration with more statistics.