Trim any excess fat from the chicken breasts and slice each into strips about 3 3/4 inches long, 1/2 inch wide, and 1/4 inch thick; do not slice thinner than 1/4 inch.
Set up three shallow bowls: place the flour in the first, the beaten eggs in the second, and combine the breadcrumbs, paprika, garlic powder, onion powder, salt, and black pepper in the third.
Heat vegetable oil in a deep fryer or heavy skillet to 350°F (use a cooking thermometer to monitor temperature).
Working in batches, dredge each chicken strip in flour and shake off the excess.
Dip the floured strip into the beaten eggs, coating it completely, then roll it in the seasoned breadcrumb mixture, pressing gently so the crumbs adhere.
Carefully lower the coated strips into the hot oil with tongs and fry for about 4–5 minutes per batch, until golden brown and cooked through.
Remove the chicken fries with tongs or a slotted spoon and drain on paper towels, then serve immediately with your preferred dipping sauce.
