HgSe is a mercury chalcogenide material of the HgX family (where X = S, Se, Te) which crystallises in the zincblende crystal phase. The electronic band structure of HgSe is indicative of a new state of matter in the condensed phase that is of great interest for fundamental physics and possibly new applications. This paper reports ab-initio calculations of the structural, electronic, magnetic, and optical properties of zincblende mercury selenide (HgSe) doped with manganese (Mn) in the inter sites HgMnxSe, with x = 0, 0.058, and 0.117, using the framework of spin-polarized density functional theory. The aim of our investigation is to discuss the different properties of this doped material in order to improve the promising new domain of spintronics with topological systems. Both the GGA+U+mBJ approach and spin-orbit coupling are used for band structure calculations and density of states. The results show a nontrivial topological semimetal order for HgSe and a ferromagnetic topological and metallic behaviour for HgMnxSe. The frequency response of optical properties shows interesting characteristics. Furthermore, the variation with concentration x of the critical point for each of the optical parameters is similar to that of the inverted band gap.