  We investigate properties of the ground-state and first radially excited
four-quark mesons $X_0$ and $X_0^{\prime}$ with a diquark-antidiquark structure
$[ud][\overline{c}\overline{s}]$ and spin-parities $J^{\mathrm{P} }=0^{+}$. Our
aim is to reveal whether or not one of these states can be identified with the
resonance $X_0(2900)$, recently discovered by the LHCb collaboration. We model
$X_0$ and $X_0^{\prime}$ as tetraquarks composed of either axial-vector or
scalar diquark and antidiquark pairs. Their spectroscopic parameters are
computed by employing the QCD two-point sum rule method and including into
analysis vacuum condensates up to dimension $ 15$. For an axial-axial structure
of $X_0^{(\prime)}$, we find partial widths of the decays $X_0^{(\prime)} \to
D^{-}K^{+}$ and $X_0^{(\prime)} \to D^{0}K^{0}$, and estimate full widths of
the states $X_0^{(\prime)}$. To this end, we calculate the strong couplings at
the vertices $ X_0^{(\prime)}DK $ in the framework of the light-cone sum rule
method. We use also technical approaches of the soft-meson approximation
necessary to analyze tetraquark-meson-meson vertices. Obtained results $m=(2545
\pm 160)~ \mathrm{MeV}$ and $m^{\prime}=(3320 \pm 120)~\mathrm{MeV}$
[$m_{\mathrm{S} }=(2663 \pm 110)~\mathrm{MeV}$ and
$m_{\mathrm{S}}^{\prime}=(3325 \pm 85)~ \mathrm{MeV}$ for a scalar-scalar
current] for the masses of the particles $ X_0$ and $X_0^{\prime}$, as well as
estimates for their full widths $ \Gamma_{0}=(140 \pm 29)~\mathrm{MeV}$ and
$\Gamma_{0}^{\prime}=(110 \pm 25)~ \mathrm{MeV}$ allow us to interpret none of
them as the resonance $X_0(2900)$ . At the same time, these predictions provide
important information about ground-state and radially excited
diquark-antidiquark structures $X_0$ and $ X_0^{\prime}$, which should be
objects of future experimental and theoretical studies.
