Place eggs in a medium saucepan, cover by with cold water by 1 inch. Bring to a boil over high heat. Remove from heat, cover with lid and let sit for 10 minutes.
Cool with cold water and ice cubes for 5 minutes. Crack and peel eggs under cold running water. Set aside.
In a bowl mash eggs finely. Add mayonnaise, mustard, salt, paprika, and sweet relish and stir to combine.