The Gemara (Sanhedrin 58a) teaches that the prohibition for Noahides to have relations with land-based non-humans is derived from the commandment: “and they shall become one flesh” i.e. they may only engage in relations that can result in bearing offspring, which would seem from this Gemara to exclude fish as well.
However, with regards to punishing a Jew, it seems from the Minchas Chinuch (Mitzvah 210) that he exempts sea creatures from the prohibitions related to non-human land animals, being that from the Gemara (Bava Kama 55a) it seems that the only prohibition that includes fish is the prohibition of Kilayim, meaning mixing different species.