In a large bowl, mix 1/4 cup sugar, yeast, salt and 2 cups flour. In a small saucepan, heat milk, shortening and water to 120°-130°. Add to dry ingredients; beat on medium speed 2 minutes. Add egg; beat on high 2 minutes. Stir in enough remaining flour to form a soft dough (dough will be sticky)., Turn dough onto a floured surface; knead until smooth and elastic, 6-8 minutes. Place in a greased bowl, turning once to grease the top. Cover and let rise in a warm place until doubled, about 1 hour., Punch down dough. Turn onto a lightly floured surface; roll to 1/2-in. thickness. Cut with a floured 3-in. round cutter. Place 2 in. apart on greased baking sheets. Cover and let rise in a warm place until nearly doubled, about 1 hour., In an electric skillet or deep fryer, heat oil to 375°. Fry doughnuts, a few at a time, until golden brown, 2-3 minutes on each side. Drain on paper towels. Cool slightly; roll in remaining 1 cup sugar., Cut a small hole in the tip of a pastry bag; insert a small pastry tip. Fill bag with jam. With a small knife, pierce a hole into the side of each doughnut; fill with jam.