In a medium saucepan combine jalapeno peppers, cranberry juice cocktail, and vinegar. Bring to boiling; reduce heat. Cover and simmer for 10 minutes. Strain mixture through a sieve, pressing with the back of a spoon to remove all the liquid (you should have 2 cups). Discard pulp.
In a 4-quart Dutch oven combine the 2 cups liquid and sugar. Bring to a full rolling boil over high heat, stirring constantly. Stir in pectin and tiny hot red peppers. Return to a full rolling boil; boil for 1 minute, stirring constantly. Remove from heat. Quickly skim off foam with a metal spoon.
Ladle at once into hot, sterilized half-pint jars, leaving a 1/4-inch headspace and making sure each jar contains one tiny red pepper. Wipe jar rims; adjust lids. Process in a boiling-water canner for 5 minutes (start timing when water begins to boil). Remove jars and cool on a wire rack until set (2 to 3 days).