In a soup pot, over medium heat, sauté onions in butter. Add cayenne and paprika, and stir until well mixed. Add chicken pieces and enough water to cover completely. Add salt and pepper to taste. Bring to a boil. Reduce heat and let simmer, covered, for 1-1/4 hours, stirring occasionally. In a tightly closed container, shake together cornstarch and the 1/3 cup water. Bring chicken mixture to a slow boil. Add sour cream, stir well. Add small amounts of cornstarch mixture until desired thickness is obtained (it shouldn't be too thick!). Remove from heat. In a large dutch oven, bring 4 quarts water to a slow boil. In a small mixing bowl, combine eggs and flour to a creamy consistency. Drop teaspoonfuls of batter in the boiling water, cooking until they float to the top. Remove dumplings from water and add to chicken mixture. Heat mixture to desired temperature and serve.