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Inspired by the recent report of the exotic states $X_{0}(2900)$ and$X_{1}(2900)$ with four different quark flavors in the $D^{-}K^{+}$ invariantmass distributions of the decay process $B^{+}\rightarrow D^{+}D^{-}K^{+}$ bythe LHCb collaboration, we systematically investigate the tetraquarks composedof $ud\bar{s}\bar{c}$ with meson-meson and diquark-antidiquark structures inthe quark delocalization color screening model. We find that the $X_{0}(2900)$can be interpreted as the molecular state $\bar{D^{*}}K^{*}$ with$IJ^{P}=00^{+}$. Moreover, two bound states are obtained by the channelcoupling calculation, with energies $2341.2$ MeV for $IJ^{P}=00^{+}$ and$2489.7$ MeV for $IJ^{P}=01^{+}$, respectively. We also extend our study to the$uc\bar{d}\bar{s}$ systems and find that there is no any bound state, so the$D_{s0}(2317)$ cannot be identified as the $DK$ molecular state in presentcalculation. Besides, several resonance states with the diquark-antidiquarkconfiguration are possible in both $ud\bar{s}\bar{c}$ and $uc\bar{d}\bar{s}$systems. All these open charm bound states and resonances are worth searchingin the future experiments.

Tetraquarks with open charm favor