Generally, Brahmins do not eat fish or other non-vegetarian food. However, Saraswat Brahmins settled in many regions of India consume fish. So why this exception? It is believed that Saraswat Brahmins are descendants of Sage Saraswat, son of Sage Dadichi and Saraswati River.
Legend has it that once there was a terrible drought for several years. Living beings found it difficult to survive. People abandoned the study of Vedas. But Saraswat was nourished by his mother Saraswati River. She fed him fish daily. He thus kept studying Vedas.
When the drought ended, people returned and flocked to him to learn the Vedas. It is said that 60,000 people learned Vedas from him. They were the ancestors of present day Saraswat Brahmin community.
As their ancestor, Sage Saraswat, had survived on fish during drought, the community eat fish.
Please note that some sub communities of Saraswat Brahmins do not consume fish.