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Heavily potassium-substituted barium iridates Ba2−xKxIrO4 (x≤0.5) and lanthanum-substituted Ba2−yLayIrO4 (y≤0.05) were prepared for the study of the carrier doping effects on the transport properties of the spin-orbit Mott state. The carrier type is holelike for the nondoped (x = y = 0) and K-doped (x>0) phases, while it is electronlike for the La-doped (y>0) phases. It was found that electron doping is more effective in decreasing the electrical resistivity. This suggests an asymmetry of the density of states between the upper and lower energies of the Fermi level. A semimetallic state emerges for the K-doped phases with x≥0.3 at ambient pressure. More conducting metallic states (ρ∼10−2 Ω cm, dρ/dT>0) were achieved under high pressure for both the K- and La-doped phases. Notwithstanding, no superconductivity was observed in the metallic states down to 4.2 K. The experimental results are discussed with respect to the electronic phase diagram calculated by Watanabe et al. [ Phys. Rev. Lett. 110 027002 (2013)]. [ABSTRACT FROM AUTHOR]