Influence of doping of mercury atom(s) on optoelectronic properties of binary cadmium chalcogenides have been investigated theoretically by designing the mercury doped cadmium chalcogenide ternary alloys in B3 phase at some specific Hg-concentrations and studying their optoelectronic properties using DFT based FP-LAPW methodology. The structural properties are computed using WC-GGA, while spin-orbit coupling included electronic and optical properties are computed using TB-mBJ, EV-GGA, B3LYP and WC-GGA exchange-correlation functionals. In addition, electronic properties of mercury chalcogenides are calculated precisely using the GGA + U functionals. The concentration dependence of lattice parameter and bulk modulus of each of the HgxCd1-xS, HgxCd1-xSe, HgxCd1-xTe alloy systems show almost linearity. For each of the alloy systems, band gap decreases almost linearly with increase in Hg-concentration in the unit cell and contribution from charge exchange to the band gap bowing is larger than that from for each of the volume deformation and structural relaxation. Also, covalent bonding exists between different constituent atoms in each compound. Optical properties of each specimen are computed from their spectra of dielectric function, refractive index, extinction coefficient, normal incidence reflectivity, optical conductivity, optical absorption coefficient and energy loss function. Several calculated results have been compared with available experimental and other theoretical data.