Using data from $\ee$ annihilation collected with the BESIII detector, we investigated the isospin violation decays of $\x$ in the processes $\ee\to\omega\jp,\pi^0\chi_{c1}$, and $\pp\jp$. We also measured the cross section for the processes $\ee\to D^{*0}D^{*-}\pi^+,\pp D^+D^-, D_s^{*+}D_s^{*-}, K^+K^-\jp$, and $K_S^0K_S^0\jp$, searching for $Y$ states in the energy-dependence of the cross section. In the analysis of $\ee\to K^+(D_s^-D^{*0}+D_s^{*-}D^0)$, we observed an excess of events above the mass threshold of $K^+$ recoil mass with a significance larger than 5$\sigma$. This marks the first candidate for a charged hidden-charm tetraquark with strangeness. We also searched for the neutral $Z_{cs}^0$ in the process $\ee\to K_S^0(D_s^+D^{*-}+D_s^{*+}D^-)$, but no signal evidence was observed. Additionally, we investigated the potential excited state $Z_{cs}'$ in the process $\ee\to K^+Z_{cs}'^-$, but no significant signals were observed.