  The low-lying $sQ\bar{q}\bar{q}$ $(q=u,\,d,\, Q=c,\,b)$ tetraquark states
with $J^P=0^+$, $1^+$ and $2^+$, and in the isoscalar and isovector sectors,
are systematically investigated in the framework of real- and complex-scaling
range of a chiral quark model, whose parameters have been fixed in advance
describing hadron, hadron-hadron and multiquark phenomenology, and thus all
results presented here are pure predictions. Each tetraquark configuration,
compatible with the quantum numbers studied, is taken into account; this
includes meson-meson, diquark-antidiquark and K-type arrangements of quarks
with all possible color wave functions in four-body sector. Among the different
numerical techniques to solve the Schr\"odinger-like 4-body bound state
equation, we use a variational method in which the trial wave function is
expanded in complex-range Gaussian basis functions, because its simplicity and
flexibility. Several compact bound states and narrow resonances are found in
both charm-strange $cs\bar{q}\bar{q}$ and bottom-strange $bs\bar{q}\bar{q}$
tetraquark sectors, most of them as a product of the strong coupling between
the different channels. The so-called $X_{0,1}(2900)$ signals, recently found
by the LHCb collaboration, are unstable in our formalism with several
candidates in the single-channel computations.
