Heat oven to 425°F (220°C). Line a sheet pan with parchment and lightly oil it. Pat the tilapia completely dry.
Mix Parmesan, panko, garlic powder, paprika, parsley, olive oil, and black pepper until evenly moistened.
Spread a very thin layer of mayonnaise or Dijon mustard over the top of each fillet. Press the Parmesan mixture firmly onto the surface.
Bake for 10 to 13 minutes, depending on thickness, until the fish flakes easily and the crust is golden. Broil briefly only if the topping needs more color.
Serve immediately with lemon wedges.