Mix olive oil and paprika in a roasting pan to form a paste.
Place lid on roasting pan or cover with aluminum foil.
Bake paprika paste in preheated oven until fragrant, about 15 minutes. Stir onion and pepper into paprika mixture; add turkey drumsticks, turning to coat. Cover roasting pan with a lid or aluminum foil and return to oven.
Continue baking until turkey is very tender and meat falls away from the bone, 4 to 5 hours.
Remove bones, leaving meat in pan, and stir in cream of mushroom soup and white wine. Simmer mixture over medium heat until hot, about 5 minutes.