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Inspired by the experimentally reported $T_{c\bar{s}}(2900)$ exotic states,the $S$-wave $\bar{q}q\bar{s}Q$ $(q=u,\,d;\,Q=c,\,b)$ tetraquarks, withspin-parity $J^P=0^+$, $1^+$ and $2^+$, in both isoscalar and isovector sectorsare systematically studied in a chiral quark model. The meson-meson,diquark-antidiquark and K-type arrangements of quarks, along with all possiblecolor wave functions, are comprehensively considered. The four-body system issolved by means of a highly efficient computational approach, the Gaussianexpansion method, along with a complex-scaling formulation of the problem todisentangle bound, resonance and scattering states. This theoretical frameworkhas already been successfully applied in various tetra- and penta-quarksystems. In the complete coupled-channel case, and within the complex-rangeformulation, several narrow resonances of $\bar{q}q\bar{s}c$ and$\bar{q}q\bar{s}b$ systems are obtained in each allowed $I(J^P)$-channels.Particularly, the $T_{c\bar{s}}(2900)$ is well identified as a $I(J^P)=1(0^+)$$\bar{q}q\bar{s}c$ tetraquark state with a dominant molecular structure.Meanwhile, more resonances in $\bar{q}q\bar{s}c$ and $\bar{q}q\bar{s}b$ systemsare also obtained within the energy regions $2.4-3.4$ GeV and $5.7-6.7$ GeV,respectively. The predicted exotic states, which are an indication of a richercolor structure when going towards multiquark systems beyond mesons andbaryons, are expected to be confirmed in future high-energy particle andnuclear experiments.

The $\mathbf{\bar{q}q\bar{s}Q}$ $\mathbf{(q=u,\,d;\,Q=c,\,b)}$ tetraquark system in a chiral quark model