The existence of a photon-like massive particle, the gamma ' or dark photon, is postulated in several extensions of the Standard Model to explain some recent puzzling astrophysical observations, as well as to solve the sofar unexplained deviation between the measured and calculated values of the muon anomaly. The dark photon, unlike the conventional photon, would have mass and would be detectable via its mixing with the latter. We present a search for the e super(+)e super(-) decay of such a hypothetical particle, 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 ( member of super(2)) at 90% CL has been obtained for the mass range M(U)= 0.02 - 0.55 GeV/c super(2) and is compared with the present world data set. Furthermore, an improved upper limit of 2.3 x 10 super(-6) at 90% CL has been set on the branching ratio of the helicity-suppressed direct decay of the eta meson eta arrow right e super(+)e super(-).