There is a well-known prohibition of eating fish and meat together, as discussed by the Gemara and Poskim.
Cooking Fish in a Meat Pot
Although it is prohibited to cook a dairy dish in a meat pot as we have discussed in a previous Halacha, nevertheless, Maran Rabbeinu Ovadia Yosef zt”l writes that there is no prohibition to fry fish in a meat pan or to cook fish in a pot that is usually used to cook meat, for the reason behind the prohibition to eat fish and meat together is because of the danger involved (as we have explained in the previous Halacha) and this danger only applies when actual fish and meat are present; however, the mere flavor of the meat which was absorbed by the pot is not sufficient to create a hazard.
Baking Fish and Meat Next to One Another in an Oven
Baking fish and meat next to one another in the same oven is also prohibited because of the danger involved, for both of their flavors mix with one another and they are both somewhat tangible. Nevertheless, if one mistakenly placed a tray of fish and a tray of meat in the oven to bake at the same time, one may act leniently and eat from them both since there are several doubts regarding this law which allow us to rule leniently on this matter once this has already occurred. Nonetheless, the great Rishon Le’Zion, Moreinu Hagaon Harav Yitzchak Yosef Shlit”a writes that several years ago, he and his father, Maran zt”l, travelled abroad and their hosts mistakenly baked fish and meat together in the same oven and Maran zt”l acted stringently and did not partake of those foods that were baked in the oven, although, as we have explained, according to the letter of the law, one may act leniently in this regard.
Grilling Fish and Meat Together on the Same Grill
Although one may not bake fish and meat together in the same oven, this only applies to our kinds of ovens which are enclosed (and not that large). However, it is permissible to grill fish and meat together on the same grill next to one another as long as they do not touch each other at all, for their respective smells and steam become dispersed in the open air and they do not come back down and become absorbed by the respective foods. (Grilling fish and meat together on the same grill over charcoals is especially common in restaurants where fish and meat are served. This is indeed permissible as long they do not come in contact with one another.)
Summary: Fish may be cooked in a clean meat pot. One may not bake fish and meat together in the same oven; rather, one must only bake them in the oven one after another, as prescribed by Halacha. One may grill fish and meat together, next to one another on the same grill as long they do not touch one another.
