In a medium saucepan, add apples, sugar and cinnamon. Cook on low heat until apples are soft, then remove from heat and mash to create a thick applesauce. Set aside.
In a separate bowl, sift flour and salt. Cut in shortening. Add water and mix until dough sticks together and you can form a ball. Dump dough onto a well-floured surface and roll it out to about 1/8 of an inch thick. Cut out 4-inch circles with a large cookie or biscuit cutter.
On each round drop 1 large tablespoon of apple mixture. Using your finger, moisten edges of dough. Fold in half then press edges closed with a fork.
Heat oil in a large skillet over medium-high heat. Fry pies two to three minutes on each side, until golden. Drain on paper towels and, while still hot, sprinkle with powdered sugar, if desired.
Note: If you don't want to make a dough for these pies, use canned biscuits, skip step 2, roll out biscuits and follow steps 3 and 4.
Note 2: If you don't want to deal with cooking apples, you can also use apple pie filling.