Line a baking sheet with parchment paper and place the fish on top. Drizzle the fish evenly with 1 tablespoon olive oil. Mix the paprika, garlic powder, onion powder, 1 teaspoon salt and a few grinds of black pepper in a small bowl. Sprinkle the mixture evenly over each of the fillets. Bake until the fish is opaque and can be easily flaked with a fork, about 10 minutes. Let cool until warm, about 10 minutes.
Flake the fish (leave the skin on the baking sheet; the meat should easily pull away from it) and transfer to a medium bowl (you should have about 339 grams fish). Add the panko, mayonnaise, capers, dill, chives, lemon zest, celery, 1 teaspoon salt and a few grinds black pepper and mix to combine.
Form the mixture into tablespoon-sized patties (about 16 grams each). (You should get 20 to 24 patties.) Heat the remaining 3 tablespoons oil in a large skillet over medium-high heat. Working in two batches, fry the patties until golden brown and can easily pull away from the pan, about 2 minutes per side. Transfer to a paper towel-lined plate and repeat with the remaining patties. Dollop with some sour cream, a few sprigs of dill or sliced cornichons on top and secure with a toothpick. Serve immediately.