The prosecution wants Circuit Judge Debra S. Nelson to ban all testimony dealing with Martin's school suspensions, marijuana use and anything to do with a history of fighting if he had one, the Orlando Sentinel reported.
Prosecutors also want the judge to prohibit defense attorneys from introducing any social media posts Martin made or text messages he sent or received, including those on the day he was killed.
That request is expected to be the most hotly contested issue Judge Nelson must decide between now and June 10 when George Zimmerman goes on trial.
Zimmerman is charged with second-degree murder for Martin's shooting death in Sanford on Feb. 26, 2012.
The two got into a fight and the teenager ended up with a fatal gunshot wound to the chest.