I wrote the following close to a decade ago.
Calcium montmorillonite clay & the 60 mineral compounds ......
This logic or theory (I don't believe there are any scientific papers on the subject of feeding clay to fish) originates with mud/clay bottomed Koi ponds in Japan, and the belief by many Koi breeders that mud lined ponds produce better Koi than cement ponds. This logic is based on the belief that the natural mineral content found in mud enhances the fishes color & overall health, as do the natural feedstuffs found in a mud bottomed pond. With the fish feed costing over half the total costs of running a Koi farm, this would also translate into overall operation savings, especially if organic & inorganic fertilisers are added to the pond (such a chicken droppings) to maximize the natural feedstuffs found in the pond.
I don't believe that the idea of the adsorption properties of clay ever played into this concept in the early days of breeding Koi, but is more of a recent event since the promotion & sale of this clay by health gurus over the past 25 years or so. While there are scores of vendors selling clay for the use in Koi ponds, I certainly don't see many freshwater or marine people jumping on the clay bandwagon.
While adding trace mineral elements to tap water that's void in certain minerals may be beneficial to some fish, a high quality food will contain an ample amount of these trace elements & minerals in the food itself. If for whatever reason one is still concerned about this, an easy fix would be to add something as simple as a teaspoon of a natural sea salt to your tank with each water change. See above for more info on that.
