Changing State Jurisdiction for Custody

My question involves a child custody case from the State of: CA / NY

When my son's father and I did our custody agreement 4 years ago it was written in paper I was allowed to move home to NY to be with my family. Our court case currently resides in CA but my lawyer at the time suggested after I establish residency here in NY that I should change the jurisdiction so it would be easier for me to ever file papers of need be since my son is a resident in this state. How do I go about changing the jurisdiction?

You file a UCCJEA petition with the New York court asking that it take jurisdiction. The other party must be properly served and noticed.

What's the easiest way to serve the other party if they live out of state?

Hire a process server, and provide the process server with addresses where service can be effected.