Mix sugar and cinnamon together on a small plate. Brush rim of martini glass with a little lemon juice, simple syrup, or water. Place glass upside down on the plate and twist to coat rim in cinnamon sugar.
Add vodka, apple cider, pumpkin spice sauce, and lemon juice to an ice-filled shaker and shake well to combine.
Pour martini into prepared martini glass. Garnish with apple slice and more cinnamon if desired.