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We have calculated the mass spectra for the $\bar{D}_s^{(*)}D^{(*)}$molecular states and $sc\bar q\bar c$ tetraquark states with $J^P=0^+, 1^+,2^+$. The masses of the axial-vector $\bar{D}_sD^{*}$, $\bar{D}_s^{*}D$molecular states and $\mathbf{1}_{[sc]} \oplus \mathbf{0}_{[\bar q \bar{c}]}$,$\mathbf{0}_{[sc]} \oplus \mathbf{1}_{[\bar q \bar{c}]}$ tetraquark states arepredicted to be around 3.98 GeV, which are in good agreement with the mass of$Z_{cs}(3985)^-$ from BESIII \cite{besiii2020Zcs}. In both the molecular anddiquark-antidiquark pictures, our results suggest that there may exist twoalmost degenerate states, as the strange partners of the $X(3872)$ and$Z_c(3900)$. We propose to carefully examine the $Z_{cs}(3985)$ in futureexperiments to verify this. One may also search for more hidden-charmfour-quark states with strangeness not only in the open-charm$\bar{D}_s^{(*)}D^{(*)}$ channels, but also in the hidden-charm channels$\eta_c K/K^\ast$, $J/\psi K/K^\ast$.

Exotic $\bar{D}_s^{(*)}D^{(*)}$ molecular states and $sc\bar q\bar c$ tetraquark states with $J^P=0^+, 1^+, 2^+$

Exotic $\bar{D}_s^{()}D^{()}$ molecular states and $sc\bar q\bar c$ tetraquark states with $J^P=0^+, 1^+, 2^+$