Are there any types of food that have magnetic properties?

The reason why the full word is "ferromagnetic" is that magnetic substances are typically made out of iron. Iron is not really edible - you can (and have to) consume it as a trace element, but the daily dose is a few milligrams. If you put enough magnetized iron in a dish to lift it visibly, you will damage a lot of your digestive tract eating it. And that's even before the question of how you are going to orient the magnet if you have dispersed the iron in your food as some kind of powder.

There are also other metals which can be magnetic, but they are even worse for eating than iron. If there is any kind of space-age material that is magnetic without being a metal compound (I'm not on the leading edge of material science and don't know if such a thing exists), it is practically certain that it is not a food.

Levitation for presentation purposes exists, but it is done by levitating the plate, or sometimes by hiding magnets within a larger food structure (typically in cake art).