Search for the Rare Decays Dₛ^+ h^+ (h^0) e^+e^-

Using 7. 33~fb^-1 of e^+e^- collision data collected by the BESIII detector at center-of-mass energies in the range of s=4. 128 - 4. 226~GeV, we search for the rare decays Dₒ^+ h^+ (h^0) e^+e^-, where h represents a kaon or pion. By requiring the e^+e^- invariant mass to be consistent with a (1020), 0. 98<M (e^+e^-) <1. 04 ~GeV/c², the decay Dₛ^+^+, e^+e^- is observed with a statistical significance of 7. 8, and evidence for the decay Dₛ^+^+, e^+e^- is found for the first time with a statistical significance of 4. 4. The decay branching fractions are measured to be B (Dₛ^+^+, e^+e^-) = (1. 17^+0. 23-₀. ₂₁0. 03) 10^-5, and B (Dₛ^+^+, e^+e^-) = (2. 44^+0. 67-₀. ₆₂ 0. 16) 10^-5, where the first uncertainties are statistical and the second systematic. No significant signal for the three four-body decays of Dₒ^+ ^+^0e^+e^-, \ Dₒ^+ K^+^0e^+e^-, and Dₒ^+ Kₒ^0^+e^+e^- is observed. For Dₒ^+ ^+^0e^+e^-, the mass region is vetoed to minimize the long-distance effects. The 90\% confidence level upper limits set on the branching fractions of these decays are in the range of (7. 0-8. 1) 10^-5.