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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 D+s→h+(h0)e+e−, where h represents a kaon or pion. By requiring the e+e− invariant mass to be consistent with a ϕ(1020), 0.98<M(e+e−)<1.04 ~GeV/c2, the decay D+s→π+ϕ,ϕ→e+e− is observed with a statistical significance of 7.8σ, and evidence for the decay D+s→ρ+ϕ,ϕ→e+e− is found for the first time with a statistical significance of 4.4σ. The decay branching fractions are measured to be B(D+s→π+ϕ,ϕ→e+e−)=(1.17+0.23−0.21±0.03)×10−5, and B(D+s→ρ+ϕ,ϕ→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 D+s→π+π0e+e−, D+s→K+π0e+e−, and D+s→K0Sπ+e+e− is observed. For D+s→π+π0e+e−, the ϕ 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.