Preheat oven to 400° F. Line a large rimmed baking sheet with parchment. Arrange mackerel, skin side up, on baking sheet. Season mackerel with salt and pepper and drizzle with 1 tablespoon olive oil. Roast mackerel 12 to 15 minutes, or until skin crisps and fish flakes easily when pierced with a fork.
Meanwhile, set a steamer basket over 1-inch of boiling salted water in a medium saucepan. Place potatoes in basket and steam, covered, until potatoes are tender, 12 to 15 minutes. Transfer steamed potatoes to a large bowl with 1 tablespoon olive oil, 1 teaspoon sherry vinegar and parsley leaves. Season potatoes with salt and pepper.
Place egg yolks, garlic and paprika in a blender; season with salt and pepper. With motor running, pour remaining olive oil into blender jar in a thin, steady stream. Stir in remaining 2 teaspoons sherry vinegar. Serve allioli with mackerel and potatoes.