Creating true muonium via charmonium radiative decay

True muonium, the bound state of a muon and an antimuon (${\mu }^{+}{\mu }^{-}$), has long been theoretically predicted but remains experimentally elusive. We investigate the production of true para-muonium in the radiative decay of $J\mathrm{/}\psi$ meson,and analyze the prospects for detecting true muonium in current and future high-energy $e^{+}{e}^{-}$ experiments, particularly focusing on the BESIII experiment and the proposed Super Tau-Charm Facility. Although the events are rare at the super tau-charm facility, the detection of true para-muonium via $J\mathrm{/}\psi$ radiative decays could become feasible at its future updates.