Contrary to popular belief, fish is not a natural food for cats, unless your cat has been stranded on an island and the only source of food is raw fish. Pet food companies include fish in many of their products because they use the wasted products of the fish. The good parts go for human consumption. Fish given as a staple for your cat can cause your cat a nutritional deficiency. We all grew up with images of cats and fish, but it reality, the best food you can give your cat is high quality canned and dry and fresh water.
You can feasibly feed your cat in small amounts, mackeral, tuna, anchovies, salmon, crab, shrimp, but they don't need it. They want it only because when it is packaged for our use it is done so to allow the smell of it to get to us, and so it also gets to your cat. My final thought is this, with the increasing ocean pollution in the world, eating and feeding fish is getting riskier. We have a friend who works a trawler out of Dutch Harbor Alaska and lately we have gotten letters from him talking about fish being caught with huge tumors on their heads.