Preheat the oven to 400 degrees F (200 degrees C). Line a baking sheet with aluminum foil.
Cut each jalapeno lengthwise. Use a spoon to scrape the seeds and membranes out of the halves. Place jalapeno halves on the prepared baking sheet.
Combine cream cheese, horseradish, garlic powder, and paprika in a small bowl. Stuff jalapeno halves with the mixture. Wrap each jalapeno with a strip of prosciutto.
Bake in the preheated oven until peppers are slightly softened and cheese is lightly browned, 15 to 17 minutes.
Meanwhile whisk apricot preserves, water, garlic powder, and red pepper flakes together in a small saucepan over medium heat until thickened. Remove from heat and keep sauce warm.
Place jalapenos on a serving platter and drizzle apricot sauce on top.
