Six C-even states, denoted as X, with quantum numbers J(PC) = 0(-+), 1(++), or 2(++), are searched for via the e(+)e(-) -> gamma(DsDs*-/+)-D-+/- 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 root s = (4681.92 +/- 0.30) MeV. No statistically significant signal is observed in the mass range from 4.08 GeV/c(2) to 4.32 GeV/c(2). The upper limits of sigma[e(+)e(-) -> gamma X] center dot B[X -> (DsDs*-/+)-D-+/-] at a 90% confidence level are determined.