I haven't been watching lately. Did something change? The history that I know is that Carly slept with Jason when they first met, and she was also sleeping with his brother A.J. She asked Jason to lie and say that he was the baby's father, and he agreed to go along with it. Robin found out about it and blabbed to A.J. (why, I don't know since it wasn't really any of her business) and Carly ended up marrying A.J. Sonny 'rescued' her and Michael from the evil A.J. and adopted Michael as his own after torturing A.J. in to give up his parental rights. Years later, A.J. showed up alive and well.....until Sonny killed him for real, and Michael went back to using Quartermaine instead of Corinthos as his last name.
If something has changed since then, I haven't heard about it. But Jason and Michael have always been close, and Jason even got himself sent to Pentonville (prison) so that he could watch over Michael when he was sent there for killing Claudia. (Sonny's one-time wife and oldCarly)