Jason waged war with Olivia, trying to remove the custody dispute from the California court ... New York is typically less generous with child support than Cali, but on Thursday New York magistrate Adele Alexis Harris handed down her decision ... "the Court finds that it is in the interest of substantial justice that the parties' child support petition be heard in California."

It's a huge but costly move for Olivia. The DailyMail obtained legal docs filed by Olivia Thursday and confirmed by TMZ, in which her lawyers say, "While Jason can afford to spin his wheels with filing after filing, Olivia cannot," adding, "Jason should not be permitted to litigate Olivia into debt." BTW, these docs were filed before the New York judge tossed the case back to Cali, so the hearing Friday has been cancelled.

Judging from the filings, the battle between them is still raging. Olivia's lawyers wrote in their docs, "We were scheduled to start working with a family therapist in California in mid-January. I thought things were calming down and were going to move forward in a more amicable, respectful fashion."

Her lawyers went on ... "Instead I learned on January 10, 2023 that the entire time I was negotiating the parenting time schedule in California [Jason] was plotting to proceed with the New York Child Support proceeding behind my back."

As you know, things got hot last April after Jason's team served Olivia onstage at CinemaCon and a process server slapped her with legal papers stating that Jason was trying to remove the custody case to New York.