In a large bowl, combine sugar, cinnamon, yeast and 1 1/2 cup of the flour.
In a small pot, heat milk, butter and water until it reaches a temperature of 125-130 degrees F. and add to dry ingredients
Using a stand mixer, beat on medium-low speed for roughly 2 minutes.
Add in sweet potatoes and eggs, beat for an additional 2 minutes
Add in remaining 2 1/2 cups of flour a little bit at a time until a firm dough forms
Place dough in a greased bowl and flip to ensure a little of the oil gets on the top of the dough
Cover dough and allow to sit and rise in a warm place for about 1 hour, or until dough has doubled in size
Using a fist, punch down the dough and pour out onto a floured surface
Roll dough out to 1/2 inch thickness and cut circles out of dough using a doughnut cutter or the lid of a mason jar. Use your fingers to form a hole in the center of the dough
Place on a greased baking sheet and cover with plastic wrap, allowing to sit for an additional 30 minutes to rise once more
Heat oil in deep fryer to 375 F and fry doughnuts until golden brown on both sides
Drain on paper towels.
Form glaze by whisking powdered sugar and apple cider together until all clumps are gone
While doughnuts are still hot, dip into glaze on both sides and allow to dry on a wire rack
Enjoy!