Check the fillets to ensure all bones and skin have been removed. Cut the fillets into manageable pieces, if necessary.
Place the beaten eggs a bowl and set aside. Combine the flour, garlic powder, salt, and pepper in another bowl. Pour the cracker crumbs into a third bowl.
Heat the oil in a deep-fryer or large cast-iron skillet over medium-high heat to 375 degrees F (190 degrees C).
Dip the fillets into the flour mixture, then the eggs, and then the cracker crumbs and set fillets aside on a plate. Test the oil: it will crackle and pop when a cracker crumb is dropped into it. Carefully lower 2 fillets into the hot oil. Cook until browned, about 3 minutes per side, using tongs to turn the fillets. Transfer to a paper towel-lined plate and repeat with remaining fillets. Serve with fresh lemon wedges.