Search for $C$-even states decaying to ${D}_{s}^{±}{D}_{s}^{*\mp }$ with masses between 4.08 and $4.32\text{}\text{}\mathrm{GeV}/{c}^{2}$

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