Use firm-fleshed fish; catfish, snapper, blackfish, dogfish, grouper, and halibut are all good choices. Please read About Deep-Frying and Shallow-Frying Fish.
I. DEEP-FRIED
Have ready:
Heat to 370°F in a deep-fryer, deep heavy pot, or Dutch oven over medium-high heat:
Dip the fish in:
Gently lower the fish into the hot fat and fry, without crowding, until golden brown, 5 to 8 minutes. Drain on paper towels or newspaper. Serve very hot, with:
II. SHALLOW-FRIED
Have ready:
Heat to 370°F in a heavy skillet with high sides or a Dutch oven:
Dredge the fish in:
Fry, without crowding, until golden brown on both sides, 5 to 8 minutes, turning once. Drain on paper towels or newspaper. Serve very hot, as for version I.