Add the apple cider, pumpkin puree, maple syrup, cinnamon, nutmeg, and cloves to a large pot.
Whisk the mixture over medium heat until the pumpkin fully blends in and the liquid turns smooth.
Continue heating for 5 minutes, stirring now and then, until the punch is warm but not boiling.
Remove the pot from the heat and pour the punch into four glasses.
Add apple slices and a cinnamon stick to each glass before serving.