Answer: The Gemara (Pesachim 21b) teaches that one may not have any benefit from, or even own chametz over Pesach. Thus, the Shulchan Aruch (OC 443:1) writes that one must not feed one’s animal chametz over Pesach. One may not even instruct a non-Jew to do so on their behalf (ibid. 448:7).
However, the Mishna Berura (448:33) and Aruch Hashulchan (OC 448:12) write that one may sell their animal to a non-Jew for the duration of Pesach. It is best to sell the animal with one’s chametz to ensure that the transaction is carried out in a halachically accepted manner, and the animal should be removed to the non-Jew’s property. One should not sell the animal along with its chametz food as that is giving the impression that one is using a tricky loophole to feed one’s animal with chametz.
Although Ashkenazim do not eat kitniyos on Pesach, they are allowed to own and benefit from it. Thus, one may feed their animals food that contains kitniyos.
Rambam (Chametz Umatza 4:8) and the Shulchan Aruch (OC 442:4) write that one does not need to dispose of a mixture containing chametz that is totally inedible (by humans). Thus, R’ Ben Zion Abba Shaul (Ohr Lezion 3:8:5) allows one to feed one’s fish with regular fish food on Pesach, even though it contains a little chametz, as there is no way that such food can be considered edible.
Nonetheless, R’ Avrohom Blumenkrantz (Chasdei Avrohom 21) recommends one to buy kosher l’pesach food, such as dried worms, etc.
In conclusion, one should look for a safe alternative to feed one’s pet fish over Pesach that does not contain chametz.