To prepare the pie dough, beat together the butter, sugar, and salt for three minutes on medium speed in the bowl of an electric mixer. Add egg and beat for 30 seconds. Add flour and water and beat for 15 seconds. Turn off the machine, scrape down the sides of the bowl, and beat again for 10 seconds.
Scoop up dough with your hands and form into a one-inch thick disk. Wrap in plastic and refrigerate for at least one hour.
Melt butter over medium-high heat in a sauté pan. Sauté peaches and sugar until sugar is dissolved, approximately two minutes. Add the preserves, cayenne, and cinnamon; cook, stirring frequently, for 3 minutes.
Dissolve cornstarch in the schnapps and stir into hot peach mixture. Remove from heat and cool.
On a lightly floured surface, roll out dough into a 16 x 11-inch rectangle about 1 /8-inch thick. Cut out 3 1 /2-inch circles and place two teaspoons of filling in the center of each dough circle. Fold the circles in half and pinch the edges together. Refrigerate pies for 30 minutes before frying.
Heat 2 1/2 inches of vegetable oil to 350-degrees in a heavy four-quart saucepan. Fry pies 4 or 6 at a time until golden brown, 1 1/2 -2 minutes per batch. Drain on paper towels.
Keep warm in a 200-degree oven until all pies are fried. Serve immediately.