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 (μ, τ) decays, pseudoscalar meson (K,π) decays, vector meson (ϕ, J/ψ, Υ) decays, and Higgs decays, have been explored to detect CLFV. Focusing on the search for CLFV at the τ-charm region, the results of the search for J/ψ → eτ/eμ using the 10 billion J/ψ events collected by the BESIII experiment are presented. The upper limits (ULs) at the 90% confidence level are ℬ(J/ψ → e
±
τ
∓) < 7.5 × 10-8 and ℬ(J/ψ → e
±
μ
∓) < 4.5 × 10-9, respectively. Improving the previously published limits by two orders of magnitudes, the results are the most stringent CLFV searches in heavy quarkonium system.