\begin{document}$ Z_{cs}(3985)^{-} $\end{document} state, denoted as \begin{document}$ Z_{cs}^{\prime -} $\end{document}, in the process \begin{document}$ e^{+} e^{-}\rightarrow K^{+}D_{s}^{*-}D^{* 0}+c.c. $\end{document}, based on \begin{document}$ e^+e^- $\end{document} collision data collected at the center-of-mass energies of \begin{document}$ \sqrt{s}=4.661 $\end{document}, 4.682 and 4.699 GeV with the BESIII detector. The \begin{document}$ Z_{cs}^{\prime -} $\end{document} is of interest as it is expected to be a candidate for a hidden-charm and open-strange tetraquark. A partial-reconstruction technique is used to isolate \begin{document}$ K^+ $\end{document} recoil-mass spectra, which are probed for a potential contribution from \begin{document}$ Z_{cs}^{\prime -}\to D_{s}^{*-}D^{* 0} $\end{document} (\begin{document}$ c.c. $\end{document}). We find an excess of \begin{document}$ Z_{cs}^{\prime -}\rightarrow D_{s}^{*-}D^{*0} $\end{document} (\begin{document}$ c.c. $\end{document}) candidates with a significance of \begin{document}$ 2.1\sigma $\end{document}, after considering systematic uncertainties, at a mass of \begin{document}$ (4123.5\pm0.7_\mathrm{stat.}\pm4.7_\mathrm{syst.}) \,\mathrm{MeV}/c^2 $\end{document}. As the data set is limited in size, the upper limits are evaluated at the 90% confidence level on the product of the Born cross sections (\begin{document}$ \sigma^{\mathrm{Born}} $\end{document}) and the branching fraction (\begin{document}$ \mathcal{B} $\end{document}) of \begin{document}$ Z_{cs}^{\prime-}\rightarrow D_{s}^{*-}D^{* 0} $\end{document}, under different assumptions of the \begin{document}$ Z_{cs}^{\prime -} $\end{document} mass from 4.120 to 4.140 MeV and of the width from 10 to 50 MeV at the three center-of-mass energies. The upper limits of \begin{document}$ \sigma^{\rm Born}\cdot\mathcal{B} $\end{document} are found to be at the level of \begin{document}$ \mathcal{O}(1) $\end{document} pb at each energy. Larger data samples are needed to confirm the \begin{document}$ Z_{cs}^{\prime -} $\end{document} state and clarify its nature in the coming years."> Search for hidden-charm tetraquark with strangeness in <inline-formula><tex-math id="M1">\begin{document}${{\boldsymbol e}^{\bf +}{\boldsymbol e}^{\bf -}{\bf\rightarrow}{\boldsymbol K}^{\bf +} {\boldsymbol D}_{\boldsymbol s}^{\bf *-}{\boldsymbol D}^{\bf{ *0}}+{\boldsymbol {c.c.}} }$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/45fa5d48-11cd-4650-92cc-15ffbcdc50e6/CPC-2022-0564_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="//www.macurncorp.com/hepnp/article/app/id/45fa5d48-11cd-4650-92cc-15ffbcdc50e6/CPC-2022-0564_M1.png"/></alternatives></inline-formula> -
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