Spread prepared apples in single layer on paper towel–lined baking sheet and pat dry with paper towels. Combine flour, sugar, baking powder, salt, cinnamon, and nutmeg in large bowl. Whisk cider, eggs, and melted butter in medium bowl until combined. Stir apples into flour mixture. Stir in cider mixture until well mixed.
Heat oil over medium-high heat to 350 degrees. Use 1/3-cup measure to transfer batter to oil. Press batter lightly with back of spoon to flatten. Fry, adjusting burner to maintain oil temperature between 325 and 350 degrees, until deep golden brown, 2 to 3 minutes per side. Transfer fritters to wire rack set inside rimmed baking sheet. Bring oil back to 350 degrees and repeat with remaining batter. Let fritters cool 5 minutes.
Whisk powdered sugar, cider and cinnamon in a bowl until smooth. Top each fritter with 1 heaping tablespoon glaze. Let glaze set 10 minutes.