In a large mixing bowl, whisk together the flour, sugar, yeast, and salt. In another bowl, combine the eggs and milk, and whisk until blended. Gradually add the wet ingredients to the dry ingredients and knead for about 10 minutes until smooth. Let the dough rise in a warm place for 1-2 hours or until doubled in size.

While the dough is rising, prepare your desired fillings. For the pumpkin cheesecake filling, combine the pumpkin puree and cream cheese, and blend until creamy. Chill the fillings in the refrigerator for about 30 minutes.

Once the dough has risen, transfer it onto a floured surface and roll it out to about ½ inch thick. Use a round cutter to cut out circles, gathering scraps to re-roll and cut again. Place on a parchment-lined baking sheet and let them rise for another 30 minutes.

In a deep fryer or pot, heat oil to 350°F. Fry the doughnuts for 2-3 minutes per side until golden brown. Use a slotted spoon to remove them and let excess oil drain on paper towels.

When slightly cooled, roll doughnuts in cinnamon sugar or dip in glaze made from powdered sugar and apple cider. Place on a wire rack to set.