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We report a search for a heavier partner of the recently observed Zcs(3985)− state, denoted as Z′−cs, in the process e+e−→K+D∗−sD∗0+c.c., based on e+e− collision data collected at the center-of-mass energies of s√=4.661, 4.682 and 4.699 GeV with the BESIII detector. The Z′−cs is of interest as it is expected to be a candidate for a hidden-charm and open-strange tetraquark. A partial-reconstruction technique is used to isolate K+ recoil-mass spectra, which are probed for a potential contribution from Z′−cs→D∗−sD∗0 (c.c.). We find an excess of Z′−cs→D∗−sD∗0 (c.c.) candidates with a significance of 2.9σ, after considering systematic uncertainties, at a mass of (4123.5±0.7stat.±1.1syst.)MeV/c2. As the data set is limited in size, the upper limits are evaluated at the 90% confidence level on the product of the Born cross section and the branching fraction of Z′−cs→D∗−sD∗0, σBorn⋅B at the three energy points, under different assumptions of the Z′−cs mass from 4.120 to 4.140 MeV and of the width from 10 to 50 MeV. Under various mass and width assumptions, the upper limits of σBorn⋅B are found to lie in the range of 2∼6, 3∼7 and 3∼6 pb at s√=4.661, 4.682 and 4.699 GeV, respectively. The larger data samples that will be collected in the coming years will allow a clearer picture to emerge concerning the existence and nature of the Z′−cs state.