The fourth Standard Model (SM) family quarks and weak iso-singlet quarks predicted by E₆ GUT are considered. The spin-average of the pseudoscalar η₄(n¹S₀) and vector ψ₄(n³S₁) quarkonium binding masses of the new mesons formed by the fourth Standard Model (SM) family and iso-singlet E₆ 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 Schrödinger 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.