AJ Quartermaine was briefly Sonny's brother-in-law. Wanting to get revenge on Sonny, he went after his sister Courtney as soon as she arrived in town. He courted her for months, much to the dismay of Sonny, who knew AJ was using his sister. On the night of his wedding to Courtney, AJ tried to blackmail Sonny. He told him he wouldn't marry Courtney if Sonny gave him Michael back. Sonny refused.
Sonny's hate for AJ goes back many years. When Carly and AJ had a fight at the Quartermaines, she lost her balance and fell down the stairs. Sonny and Carly's baby died as a result. Sonny blames AJ for the death of his child. Sonny has wanted to "take care" of AJ many times, but has declined because AJ is Michael's biological father.
AJ kidnapped and brainwashed Michael, causing him extreme trauma and shock. AJ was killed by Dr. Thomas when he returned to Port Charles.
AJ returned to Port Charles in 2012. He was faking his death. In 2014, Sonny kills AJ when he walks in on him chocking Ava Jerome.