In a mixing bowl, dissolve yeast in warm water. Add milk, butter, 1/3 cup sugar, egg yolks and salt; mix well. Stir in enough flour to form a soft dough (do not knead). Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled, about 1 1/2 hours.
Punch dough down. Turn onto a lightly floured surface; knead about 10 times. Divide dough in half. Roll each portion to 1/4-inch thickness; cut with a floured 2 1/2-inch round cutter.
Place about 1/2 teaspoon jelly in the center of half of the circles; brush edges with egg white. Top with remaining circles. Press edges to seal tightly. Place on greased baking sheet. Cover and let rise until doubled, about an hour.
In an electric skillet, heat oil to 375 degrees. Fry doughnuts, a few at a time, for 1 to 2 minutes on each side or until golden brown. Drain on paper towels.
Roll doughnuts in remaining sugar while warm. Makes 16 doughnuts.