Bring a pot of water to a rolling boil, then gently lower the eggs into the water using a spoon to prevent cracking. Boil for 12 minutes to achieve fully cooked yolks with no green ring. While the eggs cook, prepare an ice bath in a large bowl with ice and cold water. Once the timer goes off, immediately transfer the eggs to the ice bath using a slotted spoon and let them chill for at least 30 minutes. This stops the cooking process and makes the eggs much easier to peel.
Remove the cooled eggs from the ice bath and gently crack the shell all over by rolling each egg on the counter. Start peeling from the wider end where the air pocket is located, and peel under cool running water to help separate the membrane from the white. Pat the peeled eggs dry with paper towels, then carefully slice each egg in half lengthwise. Using a small spoon or your thumb, gently remove the yolks and place them in a mixing bowl, being careful not to damage the delicate egg white halves.
Mash the cooked yolks in the bowl until they're completely smooth and creamy. Add the mayonnaise and mix until well combined, then stir in the prepared mustard, well-drained sweet pickle relish, apple cider vinegar, salt, onion powder, and black pepper. I like to taste the mixture at this point and adjust the mustard or vinegar to your preference—the filling should be tangy and flavorful. If the mixture seems too thick, add a tiny splash of water; if it's too loose, add a bit more mayo.
Transfer the yolk mixture to a piping bag or spoon it directly into the hollowed egg white halves, filling them generously and creating a slight mound. Sprinkle the top of each deviled egg with a light dusting of paprika for color and a subtle smoky flavor. I recommend using a small spoon to fill the eggs if you don't have a piping bag—it takes just a minute longer but gives you great control.