Brahmins from other parts of India, as far as I know, avoid eating fish. This answer (Are Brahmins who eat fish fallen Brahmins?) showed that it is indeed forbidden. So why do Brahmins from Bengal (except Vaishnavas) eat fish? They eat all kinds of fish. It is the staple food for all Bengalis.
I know that Samrta Raghunandana was the authority in that part of India. He made many exceptions and allowed many things. Did he (or any other Samrta) allow fish (all kinds of fish)?
The basis of this is the upapurana named Brihaddharma, which allowed Brahmins of Bengal to eat fish. The english translation of the book is here.
Please also see the following from the book, History of Bengali people (page 364) by Ray.
Another of Bengal's scholars, did the same; quoting two verses from the Vishnu Purana; he tried to show that, except for a few holy days, on no day was the consumption of fish or meat an abomination. According to the Brhaddharma Purana, rohita, saphan, (pufi or saphari), saphara and other white, scaly fish were edible by Brahmans. Having given a list of animal and vegetable oils and fats Jimutavihana mentioned the oil of hilsa fish and described its various uses. It would seem that in ancient times as much as today hilsa fish was one of the favourite foods of the Bengalis and that its oil was used in a number of ways. Not all fish, however, was edible by Brahmanas; they were forbidden to eat any fish that lived in mud-holes, whose mouth and head resembled a snake's (such as the bana fish), or which had no scales. There were also prohibitions against the consumption of rotten and dried fish, although the writer of the Tikasarvasva, Sarvinanda, said that the people of Bengal were very fond of eating dried fish. Such meat as snail, crab, rooster, breast of stork, duck, water-fowl, camel, cow and swine were completely forbidden, at least in the society regulated by Brahmanical law.
