We got attorney Ariel Mitchell and her client, Courtney Burgess, Thursday outside the federal courthouse in lower Manhattan and they told us they'd just finished testifying for the grand jury.

Courtney says he was initially contacted by agents from the Department of Homeland Security ... one of the federal agencies involved in the Diddy criminal case.

Mitchell says her client was subpoenaed and she claims they have evidence to corroborate some of Courtney's allegations. He's previously done interviews, claiming he has, or has seen, salacious videos of Diddy and his celebrity friends.

Plus, he says he has the unedited version of the diary allegedly written by Kim, Diddy's late ex-girlfriend and mother of 4 of his kids.

Sources with direct knowledge tell TMZ ... the subpoena from federal prosecutors asked Burgess to turn over all records, including thumb drives, hard drives, electronic storage devices, or devices containing videos and/or other files depicting Diddy.

Sounds like it was a busy day in court for Ariel and Courtney ... because she also told our photog they were going to a separate hearing to determine, what if any, evidence they needed to turn over to the feds.

Diddy's already locked up on charges of sex trafficking, racketeering and transportation to engage in prostitution ... and has pleaded not guilty.

There was a purported Kim Porter memoir on Amazon earlier this year, but it was pulled after her kids denounced it and cast doubt on its authenticity ... and, Courtney claims he has the real deal in his possession.

Ariel tells us they are going to work with Amazon to get this book published themselves ... though they don't have a timeline.