Lawyer Suing Fat Joe Arrested for Allegedly Mowing Down Joe's Process Server

More drama in the Fat Joe civil case ... his accuser's attorney, Tyrone Blackburn, just got arrested for allegedly mowing down a process server with his car in NYC.

A rep for the New York Police Department tells us ... Blackburn was taken into custody Wednesday morning and booked for assault.

Cops say it all started on the night of May 12 when Blackburn got into his vehicle as a 66-year-old messenger was serving him a complaint in the Fat Joe case.

Blackburn allegedly slammed his car into reverse and backed up, hitting the process server in the leg and causing a minor injury. The victim reported the incident to police.

Blackburn's arrest stems from a messy legal matter involving Fat Joe and the rapper's powerhouse attorney, Joe Tacopina.

Tacopina tells us ... Blackburn sent a demand letter on behalf of Terrance Dixon to Fat Joe requesting $3 million for allegedly co-writing music with the hip hop star.

Tacopina says they blew off the letter, but Blackburn followed up with another demand letter, claiming Fat Joe was messing around with minors.

Tacopina says they wanted to get out ahead of the situation so they filed a lawsuit alleging defamation and extortion against Blackburn and Dixon. That's when Tacopina hired the messenger to serve the complaint to Blackburn.

Dixon has since filed his own $20 million lawsuit against Fat Joe, accusing him of being a pedophile.