Model who claims he's the father of Kourtney Kardashian's son gets a court hearing for next month

A male model who claims he had unprotected sex with Kourtney Kardashian in 2009 claims 3-year-old Mason is HIS son and he's now filed a paternity lawsuit asking for joint custody ... TMZ has learned.

Michael Girgenti claims in legal docs -- filed Thursday and obtained by TMZ -- he met Kourtney during a photo shoot in August, 2008 (above).  Girgenti says they connected and began a texting relationship for 3 months.

Girgenti says in legal doc things heated up by March, 2009, when Kourtney allegedly told him she and then BF Scott Disick were "on the outs" and "she wanted to hang."



Girgenti's suit then describes an alleged sexual encounter in Glendale, where he says they had "unprotected vaginal sex."  He adds, "I ejaculated inside [Kourtney's] vagina."

Girgenti says 9 months later Kourtney gave birth to Mason.  He says he immediately saw a striking resemblance and tried contacting her, to no avail, so he began a media blitz to get her attention.

Girgenti's docs, filed in L.A. County Superior Court, request joint custody of Mason.  He also wants the judge to order DNA tests for Kourtney, Scott, Mason and him.  The judge set a hearing for next month.

We also know Girgenti received a letter from Kourtney's lawyer, Shawn Holley, saying his allegations are "false and defamatory."

BTW -- one of his claims in the docs is that Kourtney's second child, Penelope, doesn't look at all like Mason.  You be the judge