We propose to search the monophoton events at the BESIII detector and future Super Tau Charm Factory to probe the sub-GeV dark photon decay into lighter dark matter. We compute the cross section due to the dark photon associated a standard model photon production, and study the corresponding standard model irreducible/reducible backgrounds. By using the data about 17 fb$^{-1}$ collected at the BESIII detector since 2011, we derive new leading limits of the mixing strength $varepsilon$, $varepsilonlesssim(1.1-1.6)times 10^{-4}$, in the mass range of 0.04 GeV $lesssim m_{A^prime} lesssim$ 3 GeV. With 30 ab$^{-1}$ data, STCF running at $sqrt{s} = 2$ GeV, can probe $varepsilon$ down to 5.1$times 10^{-6}$ when $m_{A^prime}=1$ GeV. For models of scalar and fermionic light thermal dark matter production via dark photon, we present the constrains on the dimensionless dark matter parameter $y=varepsilon^2alpha_D(m_chi/m_{A^prime})^4$ as function of the DM mass $m_{chi}$ at BESIII and future STCF, conventionally assuming the dark coupling constant $alpha_D=0.5$ and $m_{A^prime}=3 m_{chi}$. We find that BESIII can exclude model of scalar, Majorana, and pseudo-Dirac (with a small splitting) DM for the mass region 0.03$sim$1 GeV, 0.04$sim$1 GeV and 0.4$sim$1 GeV respectively. For values $alpha_Dlesssim 0.005$, combining the results from 2 GeV STCF with 30 ab$^{-1}$ data and BaBar, one can exclude the above three DM models in the mass region 0.001 GeV $lesssim m_{chi} lesssim$ 1 GeV.
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