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We obtain exact Bardeen black holes to the regularized $4D$Einstein--Gauss--Bonnet (EGB) gravity minimally coupled with the nonlinearelectrodynamics (NED). In turn, we analyze the horizon structure to determinethe effect of GB parameter $\alpha$ on the minimum cutoff values of mass,$M_0$, and magnetic monopole charge, $g_0$, for the existence of a black holehorizon. We obtain an exact expression for thermodynamic quantities, namely,Hawking temperature $T_+$, entropy $S_+$, Helmholtz free energy $F_+$, andspecific heat $C_+$ associated with the black hole horizon, and they showsignificant deviations from the $4D$ EGB case owing to NED. Interestingly,there exists a critical value of horizon radius, $r_+^{c}$, corresponding tothe local maximum of Hawking temperature, at which heat capacity diverges,confirming the second-order phase transition. A discussion on the black holesof alternate regularized $4D$ EGB gravity belonging to the scalar-tensor theoryis appended.

Bardeen Black Holes in the Regularized $4D$ Einstein--Gauss--Bonnet Gravity