African pygmy hedgehogs are insectivores by nature and are oppertunistic eaters, they require a diet that complements this. They can be fed either on special hedgehog food (Spikes relish and biscuits, however this is designed for wild hedgies so is not excellent) or a good quality dry cat food, they should not be fed food that could possibly contain fish however. (When I say good quality food it should be a food in which the primary ingredients are meat, either chicken or turkey and not cereal as many cheaper cat food are based on. The food needs to be high in protein (over 30%) and low in fat (under 12%) as hedgehogs tend to become overweight very quickly. The fat content should ideally be LESS than 10%.)
Personally I feed mine on ad lib science plan light biscuits with nutritional values of 8.2% fat and 31% protein and also 40% chicken, with the biscuits they have some chicken (cooked) and vegetables/fruit and gut fed mealworms as treats.
They can have a variety of cooked meat, each hog being different, mine love chicken and turkey, but won't touch mince or steak, so each hog is individual, they also like scrambled egg made with water not milk as hedgies are lactose intolerant.
They can also be fed a variety of fruits and vegetables, inc. apple, pear, banana, peas, sweetcorn, mashed potato, broccoli and carrot, they should not be fed grapes or raisens due to the chances of renal failure occuring or nuts and seeds due to the chocking hazard. Hedgehogs are also lactose intolerant and so cannot have chocolate or milk (unless it is lactose free, although chocolate will make them overweight very quickly).
Hedgehogs also love insects and can be given either live or dried mealworms, waxworms and crickets as a supplement to their diets, but these are very very fattening and should be monitored, I give mine a few per night, but different hogs get fatter differently. Live insects are generally better than dried as you can "gut feed" the live ones meaning you can feed them on fruit and vegetables so that when your hog eats them, he gets the nutrients that the mealworms have eaten previously, they can also provide a perfect bribe for that stubborn hog, or as a treat for doing something good!
I gut feed my mealies on cabbage and broccili with oats to keep the humidity down. Cucumber will kill mealies due to its high water content and apple and lettuce will go mouldy quickly and kill the mealies and make them smell bad too.