Inspired by the recent observation of exotic resonances $X\left(4140\right)$, $X\left(4274\right)$, $X\left(4350\right)$, $X\left(4500\right)$, and $X\left(4700\right)$ reported by several experiment collaborations, we investigated the four-quark system $cs\overline{c}\overline{s}$ with quantum numbers $J^{PC}=1^{++}$ and $0^{++}$ in the framework of the chiral quark model. Two configurations, diquark-antidiquark and meson-meson, with all possible color structures are considered. The results show that no molecular state can be formed, but the resonance may exist if the color structure of the meson-meson configuration is $8\otimes 8$. In the present calculation, the $X\left(4274\right)$ can be assigned as the $cs\overline{c}\overline{s}$ tetraquark states with $J^{PC}=1^{++}$, but the energy of $X\left(4140\right)$ is too low to be regarded as the tetraquark state. $X\left(4350\right)$ can be a good candidate of the compact tetraquark state with $J^{PC}=0^{++}$. When the radial excitation is taken into account, the $X\left(4700\right)$ can be explained as the $2S$ radial excited tetraquark state with $J^{PC}=0^{++}$. As for $X\left(4500\right)$, there is no matching state in our calculation.