Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until fork-tender, about 20 minutes. Drain. Place in a bowl and refrigerate until completely cool, about 30 minutes.
Combine oil, paprika, black pepper, and salt in a mixing bowl. Cut cooled potatoes into quarters and toss into the mixture.
Preheat an air fryer to 400 degrees F (200 degrees C).
Add 1/2 the potato wedges to the air fryer basket, placing them skin-side down and being careful not to overcrowd.
Cook until golden brown, 13 to 15 minutes. Repeat with remaining wedges.