Place the smoked turkey leg, sausage, onion, garlic salt, black pepper, and seasoned salt into a large soup pot; pour in water to cover. Bring to a boil over medium heat. Reduce heat and simmer until the meat is tender, about 1 hour.
Stir the black-eyed peas into the soup, adding more water as needed to cover peas by 1 inch. Bring to a boil. Again reduce heat and simmer until the peas are tender and have begun to break apart, about 1 more hour.
Remove turkey bones and tendons from the turkey meat and discard the bones. Add sugar and simmer until the soup is slightly creamy and thickened, stirring frequently, about 10 minutes