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The decays $K^{\ast}(892)\rightarrow K_{S,L}^{0}\pi$ can be used to study CPviolation and CPT violation. The $K^{\ast}(892)$ (hereinafter referred to as$K^{\ast}$) meson can be produced via $J/\psi$ decays at BESIII. In this paper,we study CP violation and $K_S^0-K_L^0$ asymmetry in the $J/\psi$ decaysinvolving the $K^{\ast}$ meson in the final states and obtain the followingresults \begin{align} {\mathcal A}_{CP}\left(J/\psi\rightarrowK^{\ast}f_{J/\psi}\rightarrow K^0_{S}\pif_{J/\psi}\right)=\left(3.64\pm0.04\right)\times 10^{-3},\nonumber\\ {\mathcalA}_{CP}\left(J/\psi\rightarrow K^{\ast}f_{J/\psi}\rightarrow K^0_{L}\pif_{J/\psi}\right)=\left(-3.32\pm0.04\right)\times 10^{-3},\nonumber \end{align}and \begin{align} &R\left(J/\psi\rightarrow K^{\ast}f_{J/\psi}\rightarrowK^0_{S,L}\pi f_{J/\psi} \right)=\left(3.51\pm0.03\right)\times10^{-3},\nonumber\\ &R\left(J/\psi\rightarrow \bar{K}^{\ast}\bar{f}_{J/\psi}\rightarrow K^0_{S,L}\pi \bar{f}_{J/\psi}\right)=\left(-3.45\pm0.03\right)\times 10^{-3}.\nonumber \end{align} Basing ontwo cases: the samples of $10^{10}$ and $10^{12}$ $J/\psi$ events, we calculatethe expected numbers of the observed signal events on the CP violation and the$K_S^0-K_L^0$ asymmetry in the $J/\psi$ decays with $K^{\ast}$ meson in thefinal states, we find that the BESIII experiment may be able to unambiguouslyobserve CP violation and $K_S^0-K_L^0$ asymmetry for each of these two cases.We study the possibility to constraint the CPT violation parameter $z$ anddiscuss the sensitivity for the measurement of $z$ in $J/\psi$ decays with$K^{\ast}$ meson in the final states at BESIII. The sensitivity of themeasurement of $z$ depend on the measured precision of the parameters$m_L-m_S$, $\Gamma_L$, $\Gamma_S$, $p$ and $q$ and the consistence between thevalues of $t_0$ and $t_1$ and the event selection criteria in experiment.

Study of CP violation and CPT violation in $K^{\ast}(892)\rightarrow K_{S,L}^{0}\pi$ decays at BESIII