He should immediately retain the services of an attorney. If the grandmother has had possession of the child over 6 months then she has grounds to have custody of this child. However, once your boyfriend has been legally established as the father, he can always ask a judge for custody. Without knowing the details, no attorney will attempt to give you legal advice. You need a face-to-face consultation. Good luck!
In general the courts prefer frequent and continuing contact from a child's biological parents. The name on the birth certificate is not the only way that paternity is established; and, the fact that he's paying child support is clear that paternity has been established. With that, this is still a complicated question and it depends on more facts than you have explained here. You might find some more answers at softdivorce.com and if you would like to speak to an attorney for a telephone consultation, you can schedule a free 1-hour consultation with a member of our staff.
The information provided here is for general information only and this does not constitute legal advice. You should consult an attorney of your choosing to determine your specific legal options and decisions. Do not only rely on answers here - speak to an attorney.
Hire a family law attorney immediately! He has a great chance of getting custody of his child but he shouldn't delay. He will be battling the grandparents for custody and visitation just as he normally would the child's mother. It can be done but be aware the courts will likely award the grandparents visitation as they have an established relationship with the child. Good luck!