The Bet Yosef (Orah Haim § 173) writes that one may not eat fish with dairyfood as it is considered dangerous. The Shach and the Taz (Yore De’ah § 87, Orah Haim § 173) are perplexed by this position since there is no precedent for it in the Gemara. The Gemara mentions eating fish with meat as potentially dangerous, but not fish and milk, and indeed the Shulhan Aruch (Yore De’ah 87:3) rules that it is permissible. As such, the Shach and the Taz, as well as the HIDA (Mahzik Beracha) conclude that there was a publishing error and the Bet Yosef meant to write meat and fish.
Nevertheless, the Pithe Teshuva, quotes Rabbenu Behaye Ben Asher, who writes that there is danger involved with eating fish with dairy products. The Ben Ish Hai concurs with this opinion, and Rav Ovadia Yosef (Yehave Da’at, vol. 6, § 48) says that while, strictly speaking, eating fish with dairy foods is permitted, one should ideally avoid it. Rabbi Shalom Messas says that according to the letter of the law, such a combination of food is permitted, and if asked a rabbi should not declare that it is forbidden. However, he says that for those people who are concerned of potential danger, it is preferable to avoid it. Indeed, it appears as though the common Sephardic custom is to avoid eatingfish with dairy foods.
Summary: According to the strict letter of Halachic law, eating fishtogether with dairy foods is permitted. Nevertheless, one should avoid eating these foods together.