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Six C-even states, denoted as X, with quantum numbers JPC=0−+, 1±+, or 2±+, are searched for via the e+e−→γD±sD∗∓s process using (1667.39±8.84) pb−1 of e+e− collision data collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energy of s√=(4681.92±0.30) MeV. No statistically significant signal is observed in the mass range from 4.08 to 4.32 GeV/c2. The upper limits of σ[e+e−→γX]⋅B[X→D±sD∗∓s] at a 90% confidence level are determined.