Due to its low atomic mass, hydrogen is the most promising element to search for high-temperature phononic superconductors. However, metallic phases of hydrogen are only expected at extreme pressures (400 GPa or higher). The measurement of the record superconducting critical temperature of 203 K in a hydrogen-sulfur compound at 160 GPa of pressure [A.P. Drozdov, M.I. Eremets, I.A. Troyan, arXiv:1412.0460 [cond-mat.supr-con] (2014); A.P. Drozdov, M.I. Eremets, I.A. Troyan, V. Ksenofontov, S.I. Shylin, Nature 525, 73 (2015)], shows that metallization of hydrogen can be reached at significantly lower pressure by inserting it in the matrix of other elements. In this work we investigate the phase diagram and the superconducting properties of the H-S systems by means of minima hopping method for structure prediction and density functional theory for superconductors. We also show that Se-H has a similar phase diagram as its sulfur counterpart as well as high superconducting critical temperature. We predict H₃Se to exceed 120 K superconductivity at 100 GPa. We show that both H₃Se and H₃S, due to the critical temperature and peculiar electronic structure, present rather unusual superconducting properties.