Wash and peel the potatoes, sweet potatoes, apple and onion and grate them, placing them as you go, into a large bowl filled halfway with ice water. After you are finished, let it all sit for a few minutes and thoroughly drain with a strainer. Wrap all the grated ingredients in cheesecloth or a clean kitchen towel and wring energetically, squeezing out as much liquid as you can.
Transfer to a bowl and combine with eggs, ancho chile powder, salt, cinnamon, baking powder and flour. Mix well.
Fill a large, heavy casserole or skillet with ½ inch of oil and place over medium-high heat. After 3 to 4 minutes, test the oil by adding a teaspoon of the mix. If it bubbles happily all around the edges, it is ready. Working in small batches, to not crowd the casserole, spoon latkes of about 3 tablespoons each into the hot oil. (I use large serving spoon or my hands and shape them in flattened ovals.)
Cook until the first side is crisp and golden brown, about 4 to 5 minutes, and flip to the other side, letting it crisp and brown as well, about 3 to 4 minutes. Transfer to a wire rack set over a baking sheet. Once you are finished, you may keep them warm in a 250-degree oven, or you may cover and reheat later on.