Search for the rare decay $J/\psi \to \gamma {D}^{0}+c.c.$ at BESIII

Using $\left(10087±44\right)×{10}^{6}J/\psi $ events collected with the BESIII detector, we search for the rare decay $J/\psi \to \gamma {D}^{0}+c.c.$ for the first time. No significant signal is observed and the upper limit on the branching fraction is determined to be $B\left(J/\psi \to \gamma {D}^{0}+c.c.\right)<9.1×{10}^{-8}$ at 90% confidence level.