This study investigates the thermodynamic topology of dyonic AdS black holes with quasitopological electromagnetism in the Einstein-Gauss-Bonnet (EGB) gravity background. The authors use the thermodynamic topological method to classify critical points in various dimensions of spacetime. They find that a small/large black hole phase transition occurs in all dimensions, with a conventional critical point indicating a total topological charge of \(Q_t = -1\). The coupling constant \(\alpha\) introduces a complex phase structure, with triple points appearing when \(\alpha \geq 0.5\) and \(d = 6\). The critical points are classified into conventional and novel types, with the novel critical point lacking the capability to minimize the Gibbs free energy. The critical points \(C P_{1}\) and \(C P_{2}\) occur at the maximum extreme points of temperature in the isobaric curve, while \(C P_{3}\) emerges at the minimum extreme points. The number of phases at the novel critical point increases and then decreases at the conventional critical points. As \(\alpha\) increases to 1, the system has three critical points, but only \(C P_{1}\) is a physical critical point, and \(C P_{2}\) serves as a phase annihilation point. The study highlights the significant impact of the coupling constant \(\alpha\) on the phase structure of dyonic AdS black holes.This study investigates the thermodynamic topology of dyonic AdS black holes with quasitopological electromagnetism in the Einstein-Gauss-Bonnet (EGB) gravity background. The authors use the thermodynamic topological method to classify critical points in various dimensions of spacetime. They find that a small/large black hole phase transition occurs in all dimensions, with a conventional critical point indicating a total topological charge of \(Q_t = -1\). The coupling constant \(\alpha\) introduces a complex phase structure, with triple points appearing when \(\alpha \geq 0.5\) and \(d = 6\). The critical points are classified into conventional and novel types, with the novel critical point lacking the capability to minimize the Gibbs free energy. The critical points \(C P_{1}\) and \(C P_{2}\) occur at the maximum extreme points of temperature in the isobaric curve, while \(C P_{3}\) emerges at the minimum extreme points. The number of phases at the novel critical point increases and then decreases at the conventional critical points. As \(\alpha\) increases to 1, the system has three critical points, but only \(C P_{1}\) is a physical critical point, and \(C P_{2}\) serves as a phase annihilation point. The study highlights the significant impact of the coupling constant \(\alpha\) on the phase structure of dyonic AdS black holes.