First of all, we need to distinguish between kinds of fish scales. There are four kinds of scales in fish, different in shape and chemical composition:
These are found in sharks and rays, and can vary greatly in appearance. They don’t increase in size as the fish grows; instead new scales are added. Placoid scales consist of a flattened rectangular base plate which is embedded in the fish, and variously developed structures, such as spines, which project backwards on the surface.
These are found in lungfish and some fossil fishes. Cosmoid scales are similar to placoid scales and probably evolved from the fusion of placoid scales. They consist of two basal layers of bone, a layer of dentine-like cosmine, and an outer layer of vitrodentine.
These are found in fishes such as the bichirs, bowfin, paddlefish, gars, and sturgeons. Ganoid scales are usually rhomboid in shape and have articulating peg and socket joints between them.
Cycloid and ctenoid
Cycloid and ctenoid scales are found in the majority of bony fishes. The anterior part of each scale is usually overlapped by the posterior portion of the scale in front. This arrangement of overlapping scales gives the fish greater flexibility than in those species with cosmoid and ganoid scales.
Literature report that the fish scales are composed from numerous minerals and unique biological materials such as enamel, enameloid, dentines, cosmine, ganoine, hyaline and their derivatives. I think from a nutritional point of view, eat some fish scales on fish could be useful because it might allows to introduce a part of collagen.
Collagen helps to support joints, ligaments, bones, tendons, skin, hair and nails.