For dough, combine dry ingredients in bowl; cut in shortening until mixture resembles coarse crumbs. Add water 1-2 Tbsp. at a time, stirring just until dough is moistened and forms a ball. Wrap in plastic wrap and chill for at least 1 hour.
In saucepan, combine sugar, water, and cinnamon for syrup and bring to a boil; remove from heat and add butter or margarine. Set aside.
In a small bowl, combine sugar and cinnamon for filling.
On lightly floured surface, roll dough into 18x12-inch rectangle. Cut into six 6-inch squares.
Place an apple in the center of each square; fill center with approximately 1 1/2 Tbsp. sugar-cinnamon mixture. Moisten edges of squares; fold corners to center and pinch edges together.
Place in greased 9x13 baking pan. Pour syrup over dumplings.
Bake in preheated 375 degree oven for 45-50 minutes, or until apples are tender and dumplings are lightly browned.