Kenneth Petty's inmate disciplinary history, obtained by TMZ, shows Nicki's BF was written up 18 times from 2006 to 2013 while he was serving time for a manslaughter conviction in New York.

Some of Petty's violations were major -- he got slapped with 2 violent conduct violations in 2010 for threats and fighting. Before that, he also racked up another fighting violation, and 5 violations for disobeying a direct order.

He got off to a ROUGH start too ... just one day after he entered the prison he got tagged for creating a disturbance.

There was also a 2009 incident where he was cited for 9 separate violations, and got 4 months in solitary as punishment. Mostly though ... he lost phone, recreation and commissary privileges for bad behavior.

As you know, Minaj's BF was convicted of first-degree attempted rape in 1995 when he was 16. He served almost 4 years for that ... before the 2006 manslaughter conviction.

Still, the man did his time ... and our Nicki sources say she believes Kenny -- an old flame from Queens -- has changed, and she's happier than she's been in years.