Add the the sugar, cinnamon sticks and 1 cup water to a medium saucepan over medium-high heat.
Bring the mixture a boil, stirring to dissolve the sugar. Continue to boil until a syrup forms, about 5 minutes. Remove the pan from the heat and let cool. Discard the cinnamon sticks.
The syrup can be made and stored in the refrigerator for up to a month.
For assembly:
In a medium saucepan over medium heat, bring the apple juice to a simmer then remove from heat.
Add 3 tablespoons of the cinnamon syrup and stir to combine. Divide the mixture into mugs and top with whipped cream and caramel syrup.