In this paper, we use the generalized off-shell Helmholtz free energy method to explore the thermodynamic properties of Bardeen black holes (BD BHs) from a topological perspective based on Duan’s topological current φ-mapping. We consider various structures of BD BHs, including regular BD-AdS BHs, BDAdS BHs in Kiselev’s model of quintessence, BD BHs in massive gravity (MG), and BD BHs in 4D Einstein–Gauss–Bonnet (EGB) gravity. We demonstrate that these BHs have one topological classification (TC), i.e., TC is +1 for all BHs considered, and the addition of MG or GB terms, etc., does not change the topological numbers.
