Semiclassical Quantization Condition of the Energy Levels for the Relativistic System of Two Fermions with Arbitrary Masses

New semiclassical quantization conditions of the energy levels are obtained for the relativistic systems of two fermions of arbitrary masses interacting by means of the singular conffining Coulomb-like potential. Quantization conditions of the energy levels were found for the pseudoscalar, vector, and pseudovector mesons. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of two relativistic spin particles with arbitrary masses.