In this paper, we use Bekenstein entropy and study thermodynamic quantities and phase transition for the charged BTZ black hole. Then, we apply the Sharma–Mittal (SM) entropy and calculate some thermodynamic quantities. Here, we note that in case of R ≤ δ, the SM entropy is same as the known corrected entropy. Also, we investigate P−V critically and phase transition of this corrected black hole and show that the critical points of corrected black hole are similar to Van der Waals fluid. We compare phase transition of corrected and uncorrected entropies to each other. Finally, we study the effect of SM entropy on the global and local stability in the extended phase space. Here, we also compare the obtained results of corrected entropy with respect to uncorrected entropy.
