Whisk together sugar and cinnamon until well combined. Set aside.
In a small saucepan, bring the cider to a boil over medium-high heat. Boil until reduced to 1 cup, about 45 minutes. Transfer to a heat-proof mixing bowl and cool to room temperature.
To cooled cider, whisk in sugars, eggs, and melted butter until well combined.
In another bowl, whisk together flour, baking powder, salt, baking soda, and spices. Pour cider mixture into the flour mixture and stir together until fully combined.
Cover dough and chill until firm to the touch, about 2 hours or up to 12 hours.
Once the dough is chilled, place a wire rack inside a rimmed baking sheet. Fill a Dutch oven with 3-inches of oil. Heat over medium heat to 350F.
While oil is heating, scrape the chilled dough out onto a very well-floured surface. Flour the top of the dough and pat to ½-inch thickness. Cut out rounds using a 3-inch donut cutter or a 3-inch round cookie cutter along with a 1-inch cutter to cut holes in the center of each round dipped in flour. (The dough will be very sticky. Don’t be afraid to use more flour on your surface if you need it!)
Working a few at a time, fry donuts in the hot oil until golden brown, about 1 to 2 minutes per side for large donuts and 1 minute for the donut holes. Transfer to the wire rack to drain for a few minutes. Toss warm donuts in the cinnamon sugar. These donuts are best if consumed within a few hours of frying.