Mix all ingredients for the sauce in a bowl until fully combined.
Mince the chicken into small pieces or place in a food processor and pulse until finely chopped into small pieces (do not over process).
Combine chicken pieces, seasoning rub, paprika, onion, celery, cheese, tarragon, breadcrumbs, egg, mayo, and garlic powder in a bowl.
Preheat a skillet or nonstick pan over medium heat. Once hot, add the oil. Use a 1/4-cup measuring cup to scoop even size portions of the mixture into the skillet. Press down on each fritter slightly to form a small patty. Cook until no longer pink in the center and fritters are golden brown, 3 to 4 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees. Work in batches if needed.
Remove fritters and drain on a paper towel-lined plate.
Drizzle sauce over top. Garnish with parsley.