The recent research work of two-flavor quarks with magnetised Polyakov–Nambu–Jona–Lasinio (mPNJL) model has been upgraded with the inclusion of a finite chemical potential in the temperature-dependent quark mass and the chemical potential in the interaction potential of Lagrangian density in continuation of the work of Dahiya and Singh (Pramana – J. Phys. 94:120 (2020)). The thermodynamic quantity like equation of state (EOS) and its relevant thermodynamic properties after the inclusion of the finite chemical potential in the temperature-dependent quark mass and potential are represented in the results. The outputs from the calculations show that all the thermodynamic quantities are obtained in such a way that it is enhanced and improved from theearlier result of thermodynamic properties of zero chemical potential. It means that the chemical potential really plays the role of upgradation in the outputs of thermodynamic parameters in comparison to the output produced bythe absence of chemical potential in the thermal mass and potential of the Lagrangian density.