The fourth Standard Model (SM) family quarks and weak iso-singlet quarks predicted by E-6 GUT are considered. The spin-average of the pseudoscalar eta(4)(n(1)S(0)) and vector psi(4)(n(3)S(1)) quarkonium binding masses of the new mesons formed by the fourth Standard Model (SM) family and iso-singlet E-6 with their mixings to ordinary quarks are investigated. Further, the fine and hyperfine mass splittings of the these states are also calculated. We solved the Schrodinger equation with logarithmic-and Martin potentials using the shifted large-N expansion technique. Our results are compared with other models to gauge the reliability of the predictions and point out differences.