We report a study of the processes of e^{+}e^{-}→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  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 sqrts=4.681  GeV. The structure matches a mass-dependent-width Breit-Wigner line shape, whose pole mass and width are determined as (3982.5_{-2.6}^{+1.8}±2.1)  MeV/c^{2} and (12.8_{-4.4}^{+5.3}±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 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.