Peel and dice apples; seed and dice orange and lemon (do not peel). Seed and chop jalapeño peppers.
Cook sugar in a heavy saucepan over medium heat, stirring constantly, until sugar melts and turns a deep-golden color. Carefully stir in apple, orange, lemon, and pepper (mixture will lump but become smooth with further cooking); reduce heat, and simmer, stirring constantly, 5 to 8 minutes or until apple is tender. Stir in cranberries, and simmer, stirring often, 5 to 8 more minutes or until about half of cranberries have popped. Remove from heat; cool. Cover and chill up to 1 week.