This paper investigates the role of topological photon spheres in constraining the parameters of black holes. It explores the existence and characteristics of topological photon and anti-photon spheres for various black hole models, including Einstein-Young-Mills non-minimal, AdS black holes surrounded by Chaplygin-like dark fluid, and Bardeen-like black holes in Einstein-Gauss-Bonnet gravity. The study emphasizes the necessity of photon spheres for identifying black holes and distinguishing them from naked singularities. By analyzing the topological properties of these structures, the authors propose a classification of black hole parameter spaces based on the presence and location of photon spheres. This classification helps determine the permissible ranges of parameters that define whether a solution represents a black hole or a naked singularity. The paper also discusses the implications of the existence of photon spheres for black hole stability and the validity of the Weak Cosmic Censorship conjecture. The results show that the total topological charge of a black hole is typically -1, while naked singularities have zero or +1 charges. The study highlights the importance of topological methods in understanding black hole structures and their parameters, offering a new approach to classify and constrain black hole solutions.This paper investigates the role of topological photon spheres in constraining the parameters of black holes. It explores the existence and characteristics of topological photon and anti-photon spheres for various black hole models, including Einstein-Young-Mills non-minimal, AdS black holes surrounded by Chaplygin-like dark fluid, and Bardeen-like black holes in Einstein-Gauss-Bonnet gravity. The study emphasizes the necessity of photon spheres for identifying black holes and distinguishing them from naked singularities. By analyzing the topological properties of these structures, the authors propose a classification of black hole parameter spaces based on the presence and location of photon spheres. This classification helps determine the permissible ranges of parameters that define whether a solution represents a black hole or a naked singularity. The paper also discusses the implications of the existence of photon spheres for black hole stability and the validity of the Weak Cosmic Censorship conjecture. The results show that the total topological charge of a black hole is typically -1, while naked singularities have zero or +1 charges. The study highlights the importance of topological methods in understanding black hole structures and their parameters, offering a new approach to classify and constrain black hole solutions.