This study investigates the topology of dyonic AdS black holes with quasitopological electromagnetism in the context of Einstein-Gauss-Bonnet (EGB) gravity. Using the thermodynamic topological method, the researchers classify critical points for these black holes across different spacetime dimensions. The analysis reveals that the total topological charge of the system is -1, indicating a conventional critical point. The coupling constant α plays a crucial role in determining the phase structure, with α ≥ 0.5 and d = 6 leading to the emergence of triple points. The critical points are categorized into conventional and novel types, with the latter not being able to minimize Gibbs free energy. The conventional critical points CP₁ and CP₂ are physical, while CP₃ is a novel critical point. The study also shows that as α increases, the number of phases changes, with CP₁ remaining the only physical critical point. The analysis of isobaric curves and critical temperatures confirms that CP₁ is located at the maximum temperature extreme point, while CP₃ is at the minimum. The findings highlight the importance of the coupling constant α in determining the phase structure and critical points of dyonic AdS black holes in EGB gravity. The results contribute to a deeper understanding of the thermodynamic properties and phase transitions of these black holes.This study investigates the topology of dyonic AdS black holes with quasitopological electromagnetism in the context of Einstein-Gauss-Bonnet (EGB) gravity. Using the thermodynamic topological method, the researchers classify critical points for these black holes across different spacetime dimensions. The analysis reveals that the total topological charge of the system is -1, indicating a conventional critical point. The coupling constant α plays a crucial role in determining the phase structure, with α ≥ 0.5 and d = 6 leading to the emergence of triple points. The critical points are categorized into conventional and novel types, with the latter not being able to minimize Gibbs free energy. The conventional critical points CP₁ and CP₂ are physical, while CP₃ is a novel critical point. The study also shows that as α increases, the number of phases changes, with CP₁ remaining the only physical critical point. The analysis of isobaric curves and critical temperatures confirms that CP₁ is located at the maximum temperature extreme point, while CP₃ is at the minimum. The findings highlight the importance of the coupling constant α in determining the phase structure and critical points of dyonic AdS black holes in EGB gravity. The results contribute to a deeper understanding of the thermodynamic properties and phase transitions of these black holes.