Combine cayenne pepper, paprika, salt, white pepper, black pepper, thyme, oregano, and bay leaf in a small bowl for the seasoning mix. Set aside.
Combine 3/4 cup chicken broth with onions, celery, and green pepper in a heavy 4-quart soup pot. Cook over medium- to medium-high heat until vegetables are tender, about 5 minutes. Increase heat to high. Stir in the seasoning mix, file powder, hot sauce, and garlic. Cook, stirring constantly, until mixture is fragrant and vegetables are well coated, 6 to 8 minutes.
Reduce heat to medium and stir in tomato sauce. Cook, stirring constantly, for 5 minutes. Mixture will begin to smoke and stick to the bottom of the pan; just keep stirring. Add remaining broth and bring to a boil. Add chicken and kielbasa. Reduce heat; cover and simmer, stirring occasionally, until flavors meld, 45 to 60 minutes.
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