The first name is Sicilian, the latter Roman. They are fine shallow-fried – as the son of a chip-pan incendiarist that is the only form of frying I dare undertake. If you have the nerve and a watertight insurance policy by all means try deep-frying them at home. Or you could buy a Philips Airfryer or Tefal Actifry to achieve the Vatican-approved deep-frying equivalent of safe sex.
Decent quality mozzarella is good as it is. No mozzarella gains from being cooked and turned to rubber.