  We systematically study the mass spectrum and strong decays of the S-wave
$\bar c\bar s q q$ states in the compact tetraquark scenario with the quark
model. The key ingredients of the model are the Coulomb, the linear
confinement, and the hyperfine interactions. The hyperfine potential leads to
the mixing between different color configurations, as well as the large mass
splitting between the two ground states with $I(J^P)=0(0^+)$ and
$I(J^P)=1(0^+)$. We calculate their strong decay amplitudes into the $\bar
D^{(*)}K^{(*)}$ channels with the wave functions from the mass spectrum
calculation and the quark interchange method. We examine the interpretation of
the recently observed $X_0(2900)$ as a tetraquark state. The mass and decay
width of the $I(J^P)=1(0^+)$ state are $M=2941$ MeV and $\Gamma_X=26.6$ MeV,
respectively, which indicates that it might be a good candidate for the
$X_0(2900)$. Meanwhile, we also obtain an isospin partner state $I(J^P)=0(0^+)$
with $M=2649$ MeV and $\Gamma_{X\rightarrow \bar D K}=48.1$ MeV, respectively.
Future experimental search for $X(2649)$ will be very helpful.
