Combine ground beef, turkey sausage, and egg whites in a large bowl. Add onions, garlic, black pepper, salt, cayenne, baking soda, and paprika. Mix well using your hands.

For mixture into finger-length sausages about 3/4-inch thick. Stack on a large plate, using waxed paper between the layers. Cover the plate with plastic wrap and refrigerate for at least 1 hour.

Preheat an outdoor grill for medium heat and lightly oil the grate. Grill sausages, turning as needed, until no longer pink in the center, 8 to 10 minutes.