The Fat Fish is from the book One Fish Two Fish Red Fish Blue Fish and Dr. Seuss's Book of Animals.
It and the Thin Fish meet and greet Jay and Kay who were sitting by the edge of the pond where they might have met the other fishes from before such as Red Fish, Blue Fish, Two Green Fish and the One Fish and other fishes.
It wears a yellow hat on its head.
In the Book of Animals, it is colored Yellow instead of blue and it no longer wears its hat.