On a lightly floured surface, roll out the dough to a ½” rectangle. Add the apples to one half then fold over the empty half and press down to seal in the peaches.
Using either a bench scraper or chef’s knife, slice into 1” rows then slice the opposite way to make 1” squares. Stack one side of the squares in the centers, breaking it up with the knife or bench scraper.
Section off about 1/3 cup portion sizes per fritter. Shape in the palms of your hand, using the counter to assist.
Dust individual squares of parchment paper with flour, then place each fritter on its own parchment square. Dust with flour on top of each fritter, give each a little squeeze along the edges to lock in its shape, then cover loosely with plastic wrap.
Set aside to rise 30 to 45 minutes, until nearly doubled in size.
Heat up 3” to 4” of frying oil in a skillet to 350F to 365F. Place a wire rack over a rimmed baking pan close by.
Working in small batches, use the parchment squares to help transfer the fritters into the hot oil. Fry for 1 to 3 minutes on each side, until deeply golden, using a spatula and slotted spoon to help you flip them.
Transfer with a slotted spoon to the wire rack to drain excess oils.