The measurements on a few pentaquarks states $$P_c(4440)$$ $P_c\left(4440\right)$ , $$P_c(4457)$$ $P_c\left(4457\right)$ and $$P_{cs}(4459)$$ $P_{\mathrm{cs}}\left(4459\right)$ excite our new interests about their structures. Since the masses of $$P_c(4440)$$ $P_c\left(4440\right)$ and $$P_c(4457)$$ $P_c\left(4457\right)$ are close to the threshold of $$\Sigma _c{\bar{D}}^*$$ ${\Sigma }_c{\overline{D}}^{\ast }$ , in the earlier works, they were regarded as molecular states of $$\Sigma _c{\bar{D}}^*$$ ${\Sigma }_c{\overline{D}}^{\ast }$ with quantum numbers $$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$$ $I\left(J^P\right)=\frac{1}{2}\left({\frac{1}{2}}^{-}\right)$ and $$\frac{1}{2}(\frac{3}{2}^-)$$ $\frac{1}{2}\left({\frac{3}{2}}^{-}\right)$ , respectively. In a similar way $$P_{cs}(4459)$$ $P_{\mathrm{cs}}\left(4459\right)$ is naturally considered as a $$\Xi _c{\bar{D}}^*$$ ${\Xi }_c{\overline{D}}^{\ast }$ bound state with $$I=0$$ $I=0$ . Within the Bethe-Salpeter (B-S) framework we systematically study the possible bound states of $$\Lambda _c\bar{D}^*$$ ${\Lambda }_c{\overline{D}}^{\ast }$ , $$\Sigma _c{\bar{D}}^*$$ ${\Sigma }_c{\overline{D}}^{\ast }$ , $$\Xi _c{\bar{D}}^*$$ ${\Xi }_c{\overline{D}}^{\ast }$ and $$\Xi _c'{\bar{D}}^*$$ ${\Xi }_c^{\prime }{\overline{D}}^{\ast }$ . Our results indicate that $$\Sigma _c{\bar{D}}^*$$ ${\Sigma }_c{\overline{D}}^{\ast }$ can form a bound state with $$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$$ $I\left(J^P\right)=\frac{1}{2}\left({\frac{1}{2}}^{-}\right)$ , which corresponds to $$P_c(4440)$$ $P_c\left(4440\right)$ . However for the $$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$$ $I\left(J^P\right)=\frac{1}{2}\left({\frac{3}{2}}^{-}\right)$ system the attraction between $$\Sigma _c$$ ${\Sigma }_c$ and $${\bar{D}}^*$$ ${\overline{D}}^{\ast }$ is too weak to constitute a molecule, so $$P_{c}(4457)$$ $P_c\left(4457\right)$ may not be a bound state of $$\Sigma _c{\bar{D}}^*$$ ${\Sigma }_c{\overline{D}}^{\ast }$ with $$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$$ $I\left(J^P\right)=\frac{1}{2}\left({\frac{3}{2}}^{-}\right)$ . As $$\Xi _c{\bar{D}}^*$$ ${\Xi }_c{\overline{D}}^{\ast }$ and $$\Xi _c'{\bar{D}}^*$$ ${\Xi }_c^{\prime }{\overline{D}}^{\ast }$ systems we take into account of the mixing between $$\Xi _c$$ ${\Xi }_c$ and $$\Xi '_c$$ ${\Xi }_c^{\prime }$ and the eigenstets should include two normal bound states $$\Xi _c{\bar{D}}^*$$ ${\Xi }_c{\overline{D}}^{\ast }$ and $$\Xi _c'{\bar{D}}^*$$ ${\Xi }_c^{\prime }{\overline{D}}^{\ast }$ with $$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$$ $I\left(J^P\right)=\frac{1}{2}\left({\frac{1}{2}}^{-}\right)$ and a loosely bound state $$\Xi _c{\bar{D}}^*$$ ${\Xi }_c{\overline{D}}^{\ast }$ with $$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$$ $I\left(J^P\right)=\frac{1}{2}\left({\frac{3}{2}}^{-}\right)$ . The conclusion that two $$\Xi _c{\bar{D}}^*$$ ${\Xi }_c{\overline{D}}^{\ast }$ bound states exist, supports the suggestion that the observed peak of $$P_{cs}(4459)$$ $P_{\mathrm{cs}}\left(4459\right)$ may hide two states $$P_{cs}(4455)$$ $P_{\mathrm{cs}}\left(4455\right)$ and $$P_{cs}(4468)$$ $P_{\mathrm{cs}}\left(4468\right)$ . Based on the computations we predict a bound state $$\Xi _c'{\bar{D}}^*$$ ${\Xi }_c^{\prime }{\overline{D}}^{\ast }$ with $$I(J^P)=\frac{1}{2}(\frac{1}{2}^-)$$ $I\left(J^P\right)=\frac{1}{2}\left({\frac{1}{2}}^{-}\right)$ but not that with $$I(J^P)=\frac{1}{2}(\frac{3}{2}^-)$$ $I\left(J^P\right)=\frac{1}{2}\left({\frac{3}{2}}^{-}\right)$ . Further more accurate experiments will test our approach and results.