  Einstein-Gauss-Bonnet (EGB) gravity is an outcome of quadratic curvature
corrections to the Einstein-Hilbert gravity action in the form of a
Gauss-Bonnet (GB) term in $ D > 4$ dimensions and EGB gravity is topologically
invariant in $4D$. Recently several ways have been proposed for regularizing, a
$ D \to 4 $ limit of EGB, for nontrivial gravitational dynamics in $ 4D $.
Motivated by the importance of anti-de Sitter gravity/conformal field theory
correspondence (AdS/CFT), we analyze black holes with AdS asymptotic to
regularized $4D$ EGB gravity coupled to the nonlinear electrodynamics (NED)
field. For a static spherically symmetric \textit{ansatz} the field equations
are solved exactly, using two different approaches, for a NED Lagrangian to
obtain an identical solution$-$namely NED charged AdS black holes in $4D$ EGB
gravity which retains several known solutions. Owing to the NED charge
corrected EGB black holes, the thermodynamic quantities are also modified, and
the entropy does not obey the usual area law. We calculate the heat capacity
and Helmholtz free energy, in terms of horizon radii, to investigate both local
and global thermodynamic stability of black holes. We observe a secondary
Hawking-Page transition between the smaller thermally favoured black hole and
thermal AdS space. Our results show that the behaviour of Hawking's evaporation
abruptly halts at shorter radii regime such that the black holes do have a
thermodynamically stable remnant with vanishing temperature.
