In a large Dutch oven or kettle, combine cider, pomegranate or cranberry juice, and maple syrup or brown sugar.
For spice bag, cut a double thickness of 100-percent-cotton cheesecloth into a 12-inch square. Place the halved kumquats or orange peel, 16 inches stick cinnamon, cardamom pods, and cloves in center of cloth. Bring the corners of cloth together and tie closed with clean kitchen string. Add spice bag to cider mixture.
Bring mixture to boiling; reduce heat. Cover and simmer for 15 minutes. Remove spice bag and discard.
To serve, ladle cider into mugs. If desired, garnish with additional sliced apple, kumquats and/or cinnamon sticks.