Place potatoes in a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until just tender, 15 to 20 minutes.

Drain potatoes. Transfer to baking sheets; spread in a single layer. Refrigerate until cold, about 2 hours.

Place cooled potatoes in a large bowl with eggs, mayonnaise, onion, barbecue sauce, and garlic powder; season with salt and pepper. Mix until well combined. Sprinkle with paprika.