  Using the data samples of $(1310.6\pm7.2 )\times 10^{6}$ $J/\psi$ events and
$(448.1\pm2.9)\times 10^{6}$ $\psi(3686)$ events collected with the BESIII
detector, we search for the rare decays $J/\psi \to D^{0} e^{+}e^{-} +c.c.$ and
$\psi(3686) \to D^{0} e^{+}e^{-} +c.c.$. No significant signals are observed
and the corresponding upper limits on the branching fractions at the $90\%$
confidence level are determined to be $Br(J/\psi \to D^{0} e^{+}e^{-} +c.c.)<
8.5\times 10^{-8}$ and $Br (\psi(3686) \to D^{0} e^{+}e^{-} +c.c.)<1.4\times
10^{-7}$, respectively. Our limit on $Br(J/\psi \to D^{0} e^{+}e^{-} +c.c.)$ is
more stringent by two orders of magnitude than the previous results, and the
$Br(\psi(3686) \to D^{0} e^{+}e^{-} +c.c.)$ is measured for the first time.
