In the bowl of a stand mixer fitted with the paddle attachment, add the gluten-free bread flour, potato starch, granulated sugar, milk powder, instant yeast, baking powder and salt. Mix to combine.
With the mixer running on low, slowly add the water, melted butter and eggs. Increase the speed to medium and mix for 3 minutes. The dough will resemble thick cookie dough, this is normal.
Using an oiled rubber spatula, scrape down the bottom and sides of the bowl. Cover the bowl tightly with plastic wrap and let rise in a warm place for 45-60 minutes.
After the dough has risen, refrigerate it for 20 minutes. (Refrigerating the dough makes it easier to roll out.)
Turn out the dough onto a lightly floured surface and shape into a ball. Sprinkle with a gluten-free flour, then roll the dough out into a 18x13-inch square.
Spread the apple filling evenly over the rolled-out dough, leaving a small border around the edges.
Starting from one long side, fold the dough in half horizontally so the short sides line up and you end up with a 9x13-inch rectangle. Gently press the edges to seal.
Using a pizza cutter, slice the dough into 1-inch strips lengthwise, then crosswise to create small pieces. Divide the dough into 12 equal portions and press the pieces together to form fritters. Transfer the shaped fritters to a lightly floured baking sheet. Let rest while the oil preheats.
Fill a large heavy-bottomed pot with oil, about 3-4 inches deep. Place over medium heat until a deep-fry thermometer registers 335°F.
Line a large baking sheet with paper towels. Place a wire rack on top.
When the oil is ready, drop an apple fritter into the hot oil. Cook for 2 minutes, then turn over and cook for an additional 2 minutes or until they are golden brown.
Remove the fritter from the oil and let them drain on the prepared baking sheet. Repeat with the remaining fritters.