  Inspired by the recent experimental progress on the
$T_{c\bar{s}0}^a(2900)^{0/++}$, the fully open tetraquark spectrum with the
configuration of $[8]_{[c\bar{s}]} \otimes [8]_{[q \bar{q^\prime}]}$ is
systematically investigated by the QCD sum rules. In this article, we
concentrate on the quantum numbers $J^{P}=0^{+}/0^{-}/1^{+}/1^{-}$.
  Firstly, we construct four scalar currents ($J^{P}=0^+$) in the form of
$[8]_{[c\bar{s}]} \otimes [8]_{[u\bar{d}]}$ type tetraquark structure and
perform the analysis of the QCD sum rules, where we consider the leading order
contributions up to dimension 11 in the operator product expansion and retain
contributions linear in the strange quark mass $m_s$. Our results, $M_{0^{+}}^A
= 2.91_{-0.20}^{+0.20}~\text{GeV}$ and $M_{0^{+}}^C =
2.98_{-0.21}^{+0.20}~\text{GeV}$, are consistent with the experimentally
discovered $T_{c\bar{s}0}^a(2900)^{++}$ within error margins. Thus, our
calculation supports classifying $T_{c\bar{s}0}^a(2900)^{++}$ as a tetraquark
state with the $[8]_{[c\bar{s}]} \otimes [8]_{u \bar{d}}$ color configuration.
  Moreover, on the basis of $J^P=0^+$, we also study tetraquark states with
quantum numbers $J^P=0^-$, $1^+$, and $1^-$, predicting two new hadronic states
awaiting experimental verification for each quantum number. Their masses are as
follows: $M_{0^{-}}^{A}=3.45_{-0.10}^{+0.12}~\text{GeV}$,
$M_{0^{-}}^{D}=3.20_{-0.19}^{+0.17}~\text{GeV}$,
$M_{1^{+}}^{A}=2.95_{-0.19}^{+0.19}~\text{GeV}$,
$M_{1^{+}}^{C}={2.95_{-0.19}^{+0.19}}~\text{GeV}$,
$M_{1^{-}}^{A}={3.23_{-0.10}^{+0.11}}~\text{GeV}$ and
$M_{1^{-}}^{D}={3.23_{-0.11}^{+0.09}}~\text{GeV}$. With advances in
experimental techniques and accumulation of new data, these predicted results
are hoped to be confirmed in future experiments.
