When considering the most successful vertebrates, fishes are often regarded as the most successful group. They are the most diverse group of vertebrates, with over 30,000 species, and they occupy a wide range of ecological niches in both freshwater and marine environments.
While amphibians, reptiles, and mammals have their own successes, such as adaptations to terrestrial environments and varying ecological roles, fishes stand out due to their diversity, abundance, and the vastness of their habitats. Therefore, in terms of evolutionary success and species diversity, fishes would be the most successful vertebrates among the groups you mentioned.