Spoon yogurt into a large resealable plastic bag. Add chicken and make sure it's coated in yogurt. Squeeze bag to remove excess air and seal. Marinate in the refrigerator 8 hours to overnight.
Remove chicken from yogurt and discard yogurt. Rinse yogurt from chicken pieces and pat dry with a paper towel.
Beat milk and eggs together until smooth. Mix flour, salt, pepper, curry powder, and paprika together in a wide, shallow bowl.
Dip each chicken piece into the milk mixture and immediately press into the flour mixture to coat completely; keep coated chicken on a plate while preparing the remaining pieces.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C).
Gently lie chicken pieces into the hot oil, cooking in batches as needed to avoid overcrowding, and cook until no longer pink at the bone and the juices run clear, 10 to 15 minutes per batch. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 165 degrees F (74 degrees C).