  The observation of any charged lepton flavor violation (CLFV) process would
be a clear signal of new physics beyond the Standard Model. Various decay
modes, including lepton ($\mu, \tau$) decays, pseudoscalar meson ($K,\pi$)
decays, vector meson ($\phi, J/\psi, \Upsilon$) decays, and Higgs decays, have
been explored to detect CLFV. Focusing on the search for CLFV at the
$\tau$-charm region, the results of the search for $J/\psi\to e\tau / e\mu$
using the 10 billion $J/\psi$ events collected by the BESIII experiment are
presented. The upper limits (ULs) at the 90$\%$ confidence level are
$\mathcal{B}(J/\psi\to e^\pm\tau^\mp)<7.5\times10^{-8}$ and
$\mathcal{B}(J/\psi\to e^\pm\mu^\mp)<4.5\times10^{-9}$, respectively. Improving
the previously published limits by two orders of magnitudes, the results are
the most stringent CLFV searches in heavy quarkonium system.
