Place the cubed potatoes in a large pot and cover with cold water by 1 inch. Bring to a boil over high heat. Reduce the heat to medium-low and simmer for 10-12 minutes until potatoes are fork-tender but still firm. Drain and let cool slightly.

In a large bowl, whisk together the mayonnaise, mustard, relish, pickle juice, vinegar, sugar, salt, and pepper until well combined.

Add the warm potatoes, diced onion, and chopped hard-boiled eggs to the dressing. Gently fold everything together until the potatoes are evenly coated.

Cover and refrigerate for at least 2 hours to allow flavors to meld. Taste and adjust seasoning as needed before serving.

Transfer to a serving bowl and garnish with a light dusting of paprika. Serve chilled.