Samples with nominal compositions of Hg_0.8M_0.2Ba₂Ca₂Cu₃O_y (M=V, Cr, Mn, Mo, Ag, In, Sn, W, Re, Pb, Hf, Ta) were prepared by a conventional quartz-tube encapsulation method at ambient pressure. The 1223 phase formed in the samples with dopants except In and W. Ag, Re and Pb-doping effectively expanded the temperature range for formation reaction of the 1223 phase. For samples with V, Cr, Mn, Mo and Re, appreciable shortening in the lattice parameter c was observed. It suggested incorporation of the dopants into the 1223 phase. Magnetization measurements at 77 K revealed that an enhancement in the critical current density was achieved in the samples with Re and Mo.