Gather your ingredients, pat trout fillets dry with paper towels and sprinkle all over with salt and pepper.
In a small bowl, combine the paprika, garlic powder, and oregano. Add the flour to a large plate or pie pan. Sprinkle each trout fillet with ¼ teaspoon of the seasoning, coat with flour, then sprinkle another ¼ teaspoon of seasoning on top.
Heat oil and 1 Tablespoon of butter in large nonstick skillet over medium-high heat. Carefully add trout fillets and cook for about 2 ½ minutes on each side (a total of 5 minutes), or until the fish reaches an internal temperature of 145 degrees F using an instant-read meat thermometer.Remove skillet from heat and transfer trout fillets to a platter or individual dinner plates.
Return skillet to medium heat and whisk together remaining 2 Tablespoons of butter, chicken broth, lemon juice, and capers. Cook for 1 minute or until butter is melted.
Spoon sauce over trout fillets. Garnish with chopped parsley and serve immediately.