Koi are omnivorous and will eat a variety of foods. They will also recognise you as their provider an may take food out of your hand. koi tend to fed vertically so a deep pond or tank is required to give more room when they eat. They also like sifting through gravel to look for food. Doing so will disturb the substrate and may pollute the water quickly. So strong and reliable filters are needed to accommodation this feeding habit.
Kois don’t have a normal stomach as such. They do have special pharyngeal teeth that grinds their food. You can sense when the pharyngeal teeth working when they stop taking food and simply chew! . They chew using the teeth against the roof of the mouth. Once the food is chewed it goes straight to the intestine.
Temperature also plays an important role when feeding/ Feeding should be reduced or completely stopped if temperatures reach to low in winter. Protein rich food should be reduced and/or not feed during colder winter periods. This is because the their digestive system slows down. At higher temperatures you can increase feeding regime. but just be wary of water quality as it can deteriorate quickly.