Heat oven to 350°F. Line a 12-well muffin tin with paper liners. Whisk together flour, baking soda, cinnamon, cloves, nutmeg, and salt in a large bowl until combined.
Beat butter and sugars in a stand mixer fitted with the paddle attachment until light and fluffy, about 5 minutes. Add egg, one at a time, until well combined. Add vanilla and mix again.
Add half the buttermilk and mix on low until incorporated. Add half the flour mixture and mix on low again, just until incorporated. Repeat until all buttermilk and flour mixture have been used.
Add the apples and cinnamon chips and stir just until combined. Fill paper liners with batter and bake in the middle of the oven for 30 minutes. Remove cupcakes from the pan immediately and let cool completely. Bake remaining batter.
When cupcakes are cooled, make frosting: combine butter and powdered sugar in the bowl of a stand mixer fitted with the paddle attachment. Beat until smooth and creamy. Add maple syrup and beat until incorporated and smooth. Frost cooled cupcakes and serve.