Bring the oil, water, salt and sugar to the boil in the saucepan. Take the pot off the hob and pour in the flour all at once. Work everything through well with the dough hook on the hand mixer. Put the pot back on the hot hob and continue working until the dough loosens from the bottom as a lump.
Put the dumpling in a bowl and immediately knead in 1 egg with the hand mixer and let the mixture cool down a little. Knead in the remaining eggs one after the other until the dough is glossy.
Mix the raisins or apples into the batter as desired.
Cut off the dumplings with 2 teaspoons and fry until golden in hot oil or fat. Drain and dust with powdered sugar or cinnamon sugar.