Cheese from UHT Milk
You can use UHT milk in cheeses that don't contain rennet, basically cheeses that are formed by adding acid to milk, allowing it to curdle, and then separating the whey. Quark, Paneer, Queso Fresco and Ricotta are all cheeses of this type. Opinions differ on whether UHT milk can make good cheese of this type, but it's clear that you can achieve cheese. Serious Eats discusses the use of UHT in Ricotta here. "UHT milk does not work as well as regular pasteurized milk. It has a smaller yield, and the curds do not cling together properly. The results weren't terrible, and would do in a pinch."

Even though Mozzarella can be made without rennet, it has a reputation for being particularly troublesome with UHT milk. Pictures of UHT Mozzarella Fail 

UHT Pasteurization denatures the proteins in milk to the point that they can no longer hold the curd shape, they can't fully solidify. So you can certainly try UHT in Ricotta type cheese, you may find it perfectly tasty, but I'd recommend not even trying to make rennet cheese or Mozzarella.