Search for a $ {1}^{-+}$ molecular state via $ {e}^{+}{e}^{-}\to \gamma {D}_{s}^{+}{D}_{s1}^{-}(2536)+\mathrm{c}.\mathrm{c}.$

We search, for the first time, for an exotic molecular state with quantum numbers $ {J}^{PC}={1}^{-+}$, called $ X$, via the process $ {e}^{+}{e}^{-}\to \gamma {D}_{s}^{+}{D}_{s1}^{-}(2536)+\mathrm{c}.\mathrm{c}.$ using data samples corresponding to a luminosity of $ 5.8\text{}\text{}{\mathrm{fb}}^{-1}$ across center-of-mass energies from 4.612 to $ 4.951\text{}\text{}\mathrm{GeV}$, collected with the BESIII detector operating at the BEPCII Collider. No statistically significant signal is observed. The upper limits on the product of cross section and branching fraction $ \sigma ({e}^{+}{e}^{-}\to \gamma X)·\mathcal{B}(X\to {D}_{s}^{+}{D}_{s1}^{-}(2536)+\mathrm{c}.\mathrm{c}.)$ at 90% confidence level are reported for each energy point, assuming the $ X$ mass to be $ 4.503\text{}\text{}\mathrm{GeV}/{c}^{2}$ and the width 25, 50, 75, and $ 100\text{}\text{}\mathrm{MeV}$, respectively.