  Inspired by the states $T_{cs0}(2900)^0$, $T_{cs1}(2900)^0$,
$T^a_{c\bar{s}0}(2900)^{0}$ and $T^a_{c\bar{s}0}(2900)^{++}$ reported by the
LHCb Collaboration, we carry out a systematical investigation on the properties
of the ground and $P$-wave states $[cs][\bar{u}\bar{d}]$ and
$[cu][\bar{s}\bar{d}]$ with various spin, isospin or $U$-spin, and color
combinations in a multiquark color flux-tube model. Matching our results with
the spin-parity and mass of the states $T_{cs0}(2900)^0$ and $T_{cs1}(2900)^0$,
we can describe them as the compact states $[cs][\bar{u}\bar{d}]$ with
$I(J^{P})=1(0^+)$ and $0(1^-)$ in the model, respectively. The ground state
$T_{cs0}(2900)^0$ is mainly made of strongly overlapped an axial-vector
$[cs]_{\bar{\mathbf{3}}_c}$ and an axial-vector
$[\bar{u}\bar{d}]_{\mathbf{3}_c}$. The $P$-wave state $T_{cs1}(2900)^0$ is
dominantly consisted of a gradually separated scalar or axial vector
$[cs]_{\bar{\mathbf{3}}_c}$ and a scalar $[\bar{u}\bar{d}]_{\mathbf{3}_c}$ in
the shape of a dumbbell. Supposing the states $T^a_{c\bar{s}0}(2900)^{0}$ and
$T^a_{c\bar{s}0}(2900)^{++}$ belong to the same isospin triplet, the mass of
the state $\left [[cu]_{\bar{\mathbf{3}}_c}[\bar{s}\bar{d}]_
{\mathbf{3}_c}\right ]_{\mathbf{1}_c}$ with symmetrical $U$-spin and $J^P=0^+$
is highly consistent with that of the states $T^a_{c\bar{s}0}(2900)^{0}$ and
$T^a_{c\bar{s}0}(2900)^{++}$ in the model. After coupling two color
configurations, the state $[cu][\bar{s}\bar{d}]$ is slightly lighter than the
states $T^a_{c\bar{s}0}(2900)^{0}$ and $T^a_{c\bar{s}0}(2900)^{++}$. In
addition, we also discuss the properties of other states in the model.
