  Inspired by the newly reported $Z_{cs}(3985)^{-}$ by the BESIII
Collaboration, we systematically investigate the strange hidden-charm
tetraquark systems $cs\bar{c}\bar{u}$ with two structures: meson-meson and
diquark-antidiquark. Two quark models: the chiral quark model (ChQM) and the
quark delocalization color screening model (QDCSM) are used here. Similar
results are obtained in both two quark models. There is no any bound state in
either ChQM or QDCSM, which excludes the molecular state explanation
($D_{s}D^{*}/D_{s}^{*}D/D_{s}^{*}D^{*}$) of the reported $Z_{cs}(3985)^{-}$.
However, the effective potentials for the diquark-antidiquark
$cs\bar{c}\bar{u}$ systems shows the possibility of some resonance states with
mass range of $3916.5\sim 3964.6$ MeV for $IJ^{P}=\frac{1}{2} 0^{+}$,
$4008.8\sim 4091.2$ MeV for $IJ^{P}=\frac{1}{2} 1^{+}$, $4246.8\sim 4418.1$ MeV
for $IJ^{P}=\frac{1}{2} 2^{+}$. So the observed $Z_{cs}(3985)^{-}$ state is
possible to be explained as a compact resonance state composed of
$cs\bar{c}\bar{u}$ with $IJ^{P}=\frac{1}{2} 0^{+}$ or $IJ^{P}=\frac{1}{2}
1^{+}$. The study of the scattering process of corresponding open channels is
under way to check this conclusion.
