We present a search for the e^{+}e^{-} decay of a hypothetical dark photon, also named U vector boson, in inclusive dielectron spectra measured by HADES in the p(3.5 GeV) + p, Nb reactions, as well as the Ar (1.756 GeV/u) + KCl reaction. An upper limit on the kinetic mixing parameter squared ε ^{2} at 90% CL has been obtained for the mass range M_{U}=0.02-0.55 GeV/c^{2} and is compared with the present world data set. For masses 0.03-0.1 GeV/c^{2}, the limit has been lowered with respect to previous results, allowing now to exclude a large part of the parameter region favored by the muon g−2 anomaly. Furthermore, an improved upper limit on the branching ratio of 2.3 \times 10^{-6} has been set on the helicity-suppressed direct decay of the eta meson, η → e^{+}e^{-}, at 90% CL.