Koi
The major named varieties include:Goldfish (金魚) were developed in China more than a thousand years ago by selectively breeding Prussian carp for color mutations. By the Song dynasty (960–1279), yellow, orange, white, and red-and-white colorations had been developed. Goldfish ("Carassius auratus") and Prussian carp ("Carassius gibelio") are now considered different species. Goldfish were introduced to Japan in the 16th century and to Europe in the 17th century. Koi, though, were developed from common carp in Japan in the 1820s. Koi are domesticated common carp ("Cyprinus carpio") that are selected or culled for color; they are not a different species, but a subspecies, and will revert to the original coloration within a few generations if allowed to breed freely.
Curled-gill goldfish
The Curled-gill or Reversed-gill goldfish is another uncommon variety of fancy goldfish that has been developed by specialist enthusiasts. It owes its name from the out-turned appearance of its gill covers. This fish resembles a Ryukin. For the appearance of this goldfish, it has a fantail-shaped body with long finnage all round as well as a deeply forked tail; the color is typically metallic orange.