Pour apple cider mix into a 1/2 cup measuring cup. Top off with enough sugar to equal 1/2 cup.
Combine sugar mixture, flour, baking powder, salt, cinnamon, and nutmeg in a large bowl.
Mix milk, egg, and orange zest together in a small bowl. Pour over flour mixture; mix gently until dough comes together in a ball.
Turn dough out onto a floured work surface; pat into a rectangle about 1/2-inch thick. Cut into doughnuts using a floured doughnut cutter.
Fill a large saucepan with oil to a depth 1 1/2 inch; heat to 350 degrees F (175 degrees C). Place a few doughnuts carefully into the hot oil. Fry until deep golden, 2 to 3 minutes per side. Drain on paper towels. Repeat with remaining doughnuts.
We have determined the nutritional value of oil for frying based on a retention value of 10% after cooking. Amount will vary depending on cooking time and temperature, ingredient density, and specific type of oil used.