In a large bowl, whisk together the flour, sugar, baking powder, and salt. In another bowl, beat the eggs and then mix in the milk, melted butter, and vanilla extract until combined. Gradually add the wet ingredients to the dry ingredients, mixing until just combined.

Heat the Oil

In a deep pan or fryer, heat the oil over medium heat until it reaches 350°F (175°C).

Fry the Doughnuts

Using a spoon, drop tablespoonfuls of the batter into the hot oil. Fry until golden brown on both sides, about 2-3 minutes each. Remove the doughnuts and place them on paper towels to drain excess oil.

Fill with Jelly

Using a piping bag or a small knife, carefully fill each doughnut with your choice of jelly or jam.

Orange Icing Preparation

Make the Orange Icing

In a medium bowl, mix the powdered sugar, orange juice, and orange zest until smooth. Adjust the consistency with more orange juice or powdered sugar as needed.

Glaze the Doughnuts

Dip the tops of the filled doughnuts into the orange icing and allow excess to drip off. Place on a wire rack to set.