Place pecans in a food processor or blender; process until finely chopped. Add bread crumbs and Cajun seasoning pulsing to combine.
Transfer to a shallow dish. Place buttermilk in another shallow dish; sprinkle with cayenne pepper.
Dip catfish in buttermilk and coat with pecan mixture. Set aside.
Heat butter and oil in large skillet over medium heat; when hot and melted, add catfish. Sauté until golden brown and fish flakes easily with a fork, turning once (about 10 minutes per inch of thickness).