Search for $C$-even states decaying to $D_s^{\pm }{D}_s^{*\mp }$ with masses between 4.08 and $4.32\mathrm{GeV}/c^2$

Six $C$-even states, denoted as $X$, with quantum numbers $J^{PC}=0^{-+}$, $1^{\pm +}$, or $2^{\pm +}$, are searched for via the $e^{+}{e}^{-}\to \gamma D_s^{\pm }{D}_s^{*\mp }$ process using $(1667.39\pm 8.84){\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected with the BESIII detector operating at the BEPCII storage ring at center-of-mass energy of $\sqrt{s}=(4681.92\pm 0.30)\mathrm{MeV}$. No statistically significant signal is observed in the mass range from $4.08\mathrm{GeV}/c^2$ to $4.32\mathrm{GeV}/c^2$. The upper limits of $\sigma [e^{+}{e}^{-}\to \gamma X]·B[X\to D_s^{\pm }{D}_s^{*\mp }]$ at a 90% confidence level are determined.