In a small bowl, combine the paprika, salt, garlic, onion, and Italian seasoning to create the blackening spice rub.
Pat the salmon fillets dry with paper towels, then generously coat both sides of each fillet with the spice rub, pressing it into the flesh for maximum flavor.
Heat a large cast-iron skillet over high heat until it's hot. Add the oil and butter, swirling to coat the pan evenly.
Carefully place the seasoned salmon fillets into the hot skillet, skin-side down. Cook for about 2-3 minutes until the spice rub forms a dark, flavorful crust.
Carefully flip the salmon fillets using a spatula and cook for an additional 2-3 minutes on the other side, or until the salmon is cooked to your desired level of doneness. The flesh should be opaque and flake easily with a fork.
Remove the blackened salmon from the skillet and let it rest for a minute or two.
Serve the blackened salmon hot with a squeeze of lemon or lime on top along with your choice of side dishes, such as rice, vegetables, or a fresh salad.