  Recently, some progresses have been made on the double-heavy tetraquarks in
the experiments, such as $T_{cc}$ reported by LHCb Collaboration, and
$X_{cc\bar{s}\bar{s}}$ reported by the Belle Collaboration. Coming on the heels
of our previous work about $T_{cc}$ and $T_{bb}$, we present a study on the
bound states and the resonant states of its companions $QQ\bar{q}\bar{s}$
($Q=c,b; q=u, s$) tetraquarks with strange flavor in the chiral quark model.
Two pictures, one with meson-meson picture, another with diquark-antidiquark
picture and their couplings are considered in our calculations. Isospin
violation is neglected herein. Our numerical analysis indicates that only the
state $bb\bar{u}\bar{s}$ with $\frac{1}{2}(1^+)$ is bound, with the binding
energy 3.5 MeV. Besides, we also find some resonant states for the double-heavy
strange tetraquarks with the real scaling method.
