In this paper, we employed the quasi-particle (QP) Debye mass at finite baryonic chemical potential which can be used in the medium modified heavy quark potential to solve the $N$ $N$ -dimensional Schrödinger equation. The bound state solution of the Schrödinger equation using Cornell potential been obtained by Super-Symmetry Quantum Mechanics (SUSYQM) method. The thermodynamical properties of quark matter are calculated by using baryonic chemical potential ( $μ$ $μ$ ). We found that the binding energy of quarkonia dissociates more with QP Debye mass in comparison to nonperturbative and leading order Debye mass. The medium modified form of potential (real part) has been used to study the thermodynamical properties of quark matter with different equation of states (EoSs) (i.e. pressure, energy density and speed of sound) with $μ$ $μ$ . The mass spectra of quarkonia have been also calculated in the $N$ $N$ -dimensional space and compared with the experimental data at $N = 3$ $N = 3$ . We have also calculated the dissociation temperature ( $T_{D}$ $T_{D}$ ) for the ground states of quarkonium using the dissociation criteria of thermal width.

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