In a tall-sided pot, heat the olive oil to 375 degrees F.
Dredge the anchovy fillets in the flour, then in the egg, then in the bread crumbs to coat well. Working in batches to avoid overcrowding the pot and changing the temperature of the oil, fry the fillets in the hot oil until golden brown, about 4 minutes.
Remove with a spider or slotted spoon and immediately season with salt and pepper. Drain on paper towels and serve with lemon wedges alongside.