I moved from NY to MA with my infant son. The judge granted me relocation, sole physical and legal custody and gave the father supervised visitation. We were never married, we have established paternity, but his name is not on the birth certificate. I have lived in MA 5 months now. After the 6 month period is over and me and my son are residents, is jurisdiction now in MA, or does it stay in NY? If it stays in NY, can I get it changed to MA? If so, how?

If the child's father still lives in NY, then you can't move the court order. It does not matter about the birth certificate since you already established paternity

... After the 6 month period is over and me and my son are residents, is jurisdiction now in MA, or does it stay in NY? If it stays in NY, can I get it changed to MA? If so, how?

The custody decree was originally from a New York court, right?

If so, it stays in New York, and you can't get it changed unless the non-custodial parent moves from New York.

Since Massachusetts is the only state which has not adopted the UCCJEA (http://en.wikipedia.org/wiki/Uniform_Child_Custody_Jurisdiction_And_Enforcement _Act), I am assuming that a Massachusetts court would nevertheless find it has no jurisdiction, as any UCCJEA state court would.