In a large bowl, combine the flour, granulated sugar, yeast, salt, and nutmeg. Mix well.
In a separate bowl, whisk together the warmed milk, eggs, and melted butter. Pour the wet ingredients into the dry ingredients and mix until a dough forms.
Knead the dough on a floured surface for about 5-7 minutes until smooth and elastic. Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm place for about 1 hour, or until doubled in size.
Once the dough has risen, punch it down and roll it out to about 1/2-inch thickness. Use a round cutter (about 3 inches in diameter) to cut out circles. Place the circles on a floured baking sheet and cover with a towel. Let them rise for another 30 minutes.
In a deep pot or fryer, heat vegetable oil to 350°F. Carefully drop in the donuts, a few at a time, and fry for about 1-2 minutes on each side until golden brown. Remove with a slotted spoon and drain on paper towels.
Once cooled slightly, use a piping bag or a small squeeze bottle to fill each donut with jelly. Dust the filled donuts with powdered sugar before serving.