In a medium bowl, mix together the flour, 1/4 cup sugar, the cinnamon, salt, baking powder and baking soda. Add the sparkling water, buttermilk and vanilla, and stir until the mixture forms a batter. Let rest for 15 minutes.
In a small bowl, whisk together the remaining 1/2 cup sugar and the lemon zest.
In a heavy 4 to 5-quart saucepan, heat the olive oil and vegetable oil over medium heat until a deep-fry thermometer registers 375 degrees F. (If you don't have a thermometer, a cube of bread should brown in about 3 minutes.)
Meanwhile, peel and core the apples, then cut into 1/2-inch-thick slices. Using paper towels, blot the apple slices dry.
Add the apple slices to the batter and toss until coated. Working in batches, fry the apples, turning occasionally, until golden brown, 2 to 3 minutes per batch. Drain on paper towels and sprinkle with the lemon sugar while still warm. Serve immediately.