In the bowl of a food processor, combine the ketchup and cherry preserves. Puree until smooth. Set aside or refrigerate until ready to use.
Heat the oil in a medium Dutch oven or deep saucepan over medium-high heat until it reaches 350 degrees F on a deep-fry thermometer. In a small bowl, mix together the salt and cinnamon. Using the medium-thick blade on a spiralizer, cut the potatoes into spirals.
In small batches (about 3/4 cup each), fry the potatoes, turning them as needed with a spider so they brown evenly, until they are lightly golden and crispy, 1 to 2 minutes. Remove the potato nests to a paper towel-lined tray and sprinkle with some of the salt mixture. Serve the cherry ketchup alongside the potato nests for dipping.