Search for the rare decays $D\to h\left({h}^{\left(\prime \right)}\right){e}^{+}{e}^{-}$

We search for rare decays of $D$ mesons to hadrons accompanied by an electron-positron pair ($h\left({h}^{\left(\prime \right)}\right){e}^{+}{e}^{-}$), using an ${e}^{+}{e}^{-}$ collision sample corresponding to an integrated luminosity of $2.93\text{}\text{}{\mathrm{fb}}^{-1}$ collected with the BESIII detector at $\sqrt{s}=3.773\text{}\text{}\mathrm{GeV}$. No significant signals are observed, and the corresponding upper limits on the branching fractions at the 90% confidence level are determined. The sensitivities of the results are at the level of ${10}^{-5}–{10}^{-6}$, providing a large improvement over previous searches.