In a medium saucepan, combine the water, sugar and cinnamon sticks. Boil over moderately high heat, stirring occasionally, until the sugar is dissolved, about 5 minutes. Let the syrup cool. Discard the cinnamon sticks.
In an ice-filled cocktail shaker, combine 1/2 tablespoon of the cinnamon syrup with the apple brandy, Snap liqueur and bitters. Stir well. Strain the drink into an ice-filled rocks glass and garnish with the apple slice.