In a large saucepan, combine the sugar, 1/2 cup cranberry juice, cranberries and jalapeno. Bring to a boil. Reduce heat; simmer, uncovered, for 3 minutes or until sugar is dissolved. Remove from the heat. Cover and let stand for 20 minutes. , Strain, discarding cranberries and jalapeno. Cover and refrigerate syrup for at least 2 hours or until chilled., For each serving, fill a mixing glass or tumbler three-fourths full with ice. Add 3 ounces vodka, 1 tablespoon cranberry juice and 1 tablespoon cranberry syrup; stir until condensation forms on outside of glass. Strain into a chilled cocktail glass. Repeat. Garnish with mint and cranberries if desired.