Prepare the fish fillets by patting them dry and seasoning with salt and pepper.
Set up a breading station with three bowls: one with flour, one with beaten eggs, and one with breadcrumbs.
Dredge each fish fillet in flour, shaking off excess, then dip into the egg, and finally coat with breadcrumbs.
Heat oil in a frying pan over medium-high heat until shimmering but not smoking.
Fry the coated fish for about 3 to 4 minutes per side, or until golden brown and cooked through.
Remove the fish from the oil and place on a paper towel-lined plate to drain excess oil.
For the dipping sauce, combine mayonnaise, lemon juice, and capers in a bowl and mix well.
Serve the crispy fish hot with the dipping sauce on the side.