Place cubed potatoes in a large pot, cover with water, and bring to a boil. Cook until tender, about 10-15 minutes. Drain and let cool.
Partially mash the cooked potatoes.
In a large bowl, combine mayonnaise, mustard, relish, chopped celery, celery seed, dill weed, and onion. Add cooled potatoes and eggs. Season with salt and pepper and adjust other seasonings as needed. Gently mix until well combined.
Sprinkle with paprika and green onions. Cover and refrigerate for at least 1 hour before serving to blend the flavors.