Boil the cubed potatoes in salted water until tender, about 15 minutes. Drain and let cool.
In a large bowl, mix mayonnaise, mustard, and pickle relish until smooth.
Add the cooked potatoes, chopped eggs, celery, and onion to the bowl. Gently mix until combined.
Season with salt and pepper to taste.
Chill in the refrigerator for at least 1 hour before serving.
Garnish with paprika if desired.