Koi love citrus fruit. Betty Roemer showed me how much by suggesting grapefruit slices and MAN did they like it.

Important ones seem to be fat soluble A,D,E and K - and vitamin C.

Vitamin deficiencies from missing vitamins are comparatively rare in the last two decades. This is because vitamin premixes exist in the processing of fish food that have eliminated most of the mystery and a lot of the onerous expense. Vitamins A,D,E and K when deficient result in lesions of the skin, eyes, and nervous system. Vitamin K contributes to blood clotting. How much this bears on fish is vague at best. 

Vitamin C is not so mysterious. Addition of Vitamin C to the diet of Koi and Goldfish is a "Good Thing" for several reasons. First, it's essential to the fish and contributes majorly to disease resistance. Second, food processing degrades Vitamin C so that enough of this has to be added to the food to where a surplus survives the processing of the food. Inattention on the part of the feed manufacturer to this could result in food too low in Vitamin C. Finally, if available over 180 milligrams per kilogram, some research supports that the immune system is not only supported, but dramatically enhanced.