Start by grating the potatoes and onions, then squeeze out all of the liquid. Transfer the grated potatoes and onions to a medium bowl. Add the flour, egg yolks, salt, and pepper and mix well.
In a medium saute pan over medium-high heat, heat vegetable oil and schmaltz. Form the potato mixture into 2-inch diameter patties and place in pan. Cook each latke for 3 to 4 minutes per side, or until golden brown. Repeat until all the latke mixture from the bowl has been used.