Jason Patric was just shut down by a judge in his bid to win paternity and custody rights over his son ... TMZ has learned.

Jason was locked in a bitter legal war with ex-GF Danielle Schreiber. The two were together for years but broke up in 2009. At the time they ended the relationship Jason told Danielle he didn't have any money to give her but he would give her his sperm, provided he had nothing to do with raising the child and she didn't ask for child support. 

Danielle was artificially inseminated with the help of a doctor, and Gus was born in December, 2009.  

Jason went away and had no contact with Gus, but came back in 2011. Jason and Danielle got back together ... but they broke up again. That's when he decided he wanted custody.

The trial has been going on for a week, and we've learned the judge just laid down the law -- a law that says if a man donates sperm to a woman to whom he is NOT married and she's inseminated with the help of a doctor ... the man has no paternity rights or claim of custody.

As we previously reported ... Danielle let Jason see Gus for visits, but there was no court order enforcing that.  We don't know if she will continue to let Jason see the child.

Actor Jason Patric is embroiled in a bizarre custody war, in which he donated sperm so his ex-girlfriend could have a baby, but according to the deal she could never tell anyone or ask for financial support.

TMZ has learned the facts surfaced in a court hearing earlier this month -- Patric was with on-again-off-again girlfriend Danielle Schreiber for more than a decade. They broke up in early 2009, and he allegedly told her that he didn't have any money to give her but he would give her the next best thing -- his sperm, so she could have a baby.

We're told Jason made it clear ... he would only provide his sperm if she didn't breathe a word to anyone and never asked him for child support. She agreed.

Baby Gus was born in December, 2009. In 2011, Jason and Danielle got back together but it didn't last long. They broke up in May, 2012.

Apparently, while they were together, Jason, who never paid Danielle child support, took a liking to Gus, because he filed legal docs in family court asking a judge to award him 50/50 custody.

But there's a little known law which says if an unmarried man artificially inseminates an unmarried woman with the help of a physician, he's NOT legally the dad and has no custody rights.

The judge has given Danielle temporary sole legal and physical custody of the boy. Jason has visitation rights. We're told Danielle is fine VOLUNTARILY giving Jason the right to spend time with the boy, but objects to a judge ordering visitation -- she doesn't believe Jason has or should have any LEGAL rights to custody or visitation.

The case is back in court this afternoon. We'll let you know what happens.