Our recent research work for 2 flavor magnetized PNJL model has been extended to \(2+1\) flavor quarks cooperating the finite baryonic potential in the thermal mass and magnetic field in the potential of the Lagrangian density. The evaluation of equation of state and its relevant thermodynamic properties after incorporating the finite chemical potential in the thermal mass and magnetic field in the potential are represented in the results. The results show that all the thermodynamic parameters are found to be improved by the inclusion of the finite baryonic chemical potential. The result at the finite baryonic density also conforms and improves from our earlier work without the value of baryonic chemical potential. It means that there is an up-gradation in the outputs as predicted by the presence of baryonic chemical potential in the thermal mass.
