  The low-lying $S$-wave $QQ\bar{s}\bar{s}$ ($Q=c, b$) tetraquark states with
$IJ^P=00^+$, $01^+$ and $02^+$ are systematically investigated in the framework
of complex scaling range of chiral quark model. Every structure including
meson-meson, diquark-antidiquark and K-type configurations, and all possible
color channels in four-body sector are considered by means of a commonly
extended variational approach, Gaussian expansion method. Several narrow and
wide resonance states are obtained for $cc\bar{s}\bar{s}$ and
$bb\bar{s}\bar{s}$ tetraquarks with $IJ^P=00^+$ and $02^+$. Meanwhile, narrow
resonances for $cb\bar{s}\bar{s}$ tetraquarks are also found in $IJ^P=00^+$,
$01^+$ and $02^+$ states. These results confirm the possibility of finding
hadronic molecules with masses $\sim\,0.6\,\text{GeV}$ above the noninteracting
hadron-hadron thresholds.
