  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 $\varepsilon$, $\varepsilon\lesssim(1.1-1.6)\times
10^{-4}$, 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
$y=\varepsilon^2\alpha_D(m_\chi/m_{A^\prime})^4$ 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 $\alpha_D\lesssim 0.005$, 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.
