  Open-heavy tetraquark states, especially those contain four different quarks
have drawn much attention in both theoretical and experimental fields. In the
framework of the improved chromomagnetic interaction (ICMI) model, we complete
a systematic study on the mass spectra and possible strong decay channels of
the $S$-wave open-heavy tetraquark states, $qq\bar{q}\bar{Q}$ ($q=u,d,s$ and
$Q=c,b$), with different quantum number $J^P=0^+$, $1^+$, and $2^+$. The
parameters in the ICMI model are extracted from the conventional hadron spectra
and used directly to predict the mass of tetraquark states. Several compact
bound states and narrow resonances are found in both charm-strange and
bottom-strange tetraquark sectors, most of them as a product of the strong
coupling between the different channels. Our results show the recently
discovered four different flavors tetraquark candidates $X_0(2900)$ is probably
compact $ud\bar{s}\bar{c}$ state with quantum number $J^P=0^+$. The predictions
about $X_0(2900)$ and its partners are expected to be better checked with other
theories and future experiments.
