Heat the oil in a small skillet over medium heat. Cook the capers, stirring occasionally, until browned and crisp, 4 to 5 minutes. Transfer to a paper towel–lined plate and let cool.
Halve the eggs. Scoop out the yolks and combine with the mayonnaise, salmon, yogurt, mustard, 1/2 teaspoon salt, and 1/4 teaspoon pepper.
Spoon the filling into the egg whites. Serve topped with the fried capers and more chopped smoked salmon.