The S-wave   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   tetraquarks, with spin-parities   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $  ,   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $  , and   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $  , in both isoscalar and isovector sectors, are systematically studied using a chiral quark model. The meson-meson, diquark-antidiquark, and K-type arrangements of quarks and all possible color wave functions are comprehensively considered. The four-body system is solved using the Gaussian expansion method, a highly efficient computational approach. Additonally, a complex-scaling formulation of the problem is established to disentangle bound, resonance, and scattering states. This theoretical framework has already been successfully applied in various tetra- and penta-quark systems. For the complete coupled channel and within the complex-range formulation, several narrow resonances of   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   and   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   systems are obtained, in each allowed   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $  -channel, within the energy regions of   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   GeV and   $ \bar{q}q\bar{s}Q \;\; (q=u,\,d;\,Q=c,\,b) $   GeV, respectively. The predicted exotic states, which indicate a richer color structure when going towards multiquark systems beyond mesons and baryons, are expected to be confirmed in future high-energy particle and nuclear experiments.