Using a large bowl, mix yeast into water or milk. Add sugar. Let the yeast dissolve over 10 minutes.
Melt the margarine or butter. Stir it into the yeast mixture.
Mix in the egg yolks and salt. Add flour by the cupful, mixing with a spoon at first, then kneading it gently by hand to obtain a soft dough.
Cover the bowl with plastic wrap and let the dough rise 1-1/2 hours at room temperature.
Roll the dough 1/4-inch thick on a lightly floured surface. Using a biscuit cutter or glass 2 1/2” in diameter, cut circles out of it. Gather up any scraps, re-roll them, and cut as many circles as you can out of it. Let circles rise 1/2 hour.
Use a spatula to lift the dough circles off the work surface and slide them into the hot oil. Don’t crowd them. Deep fry the circles at 400° F (200° C) for about 3 minutes, turning once. Keep a sharp eye on the doughnuts; they will burn in a second if left in the hot oil too long.
Remove the fried donuts from the oil and set to drain on a baking tray covered with paper towels.
Use a wooden skewer, the thin end of a chopstick or a toothpick to poke a hole in one side of each doughnut. Pipe 2 teaspoons of jelly in, or as much as each donut will take. Roll each donut in powdered sugar.