TMZ has obtained court documents from the case ... where J.T.'s claiming Hart initially made baseless allegations about his role in filming and disseminating the infamous 2017 sex tape that apparently featured the comedian hooking up with Montia Sabbag.

Jackson says the two came to a settlement agreement in 2021 where he says Hart agreed to make a public apology and help rehabilitate Jackson's public reputation.

J.T. says they had a public statement totally written out that Kevin would release -- but, when the time came, Jackson claims Hart deviated from the prepared statement ... including a part in the settlement that J.T. says called for Kevin to say Jackson had nothing to do with any alleged extortion plot.

Jackson says Hart's changing of the critical wording deprived him of the benefit of the deal, which was supposed to help repair his reputation and ability to work in the industry.

If you don't remember ... Jackson was hit with four charges including attempted extortion, attempted concealing and selling stolen property, unauthorized use of personal ID and identity theft in connection to the alleged leaking of the tape. The charges, however, were later dropped.

Jackson's suing Hart for breach of contract, infliction of emotional distress, and more and wants at least $12 million in damages. He tells TMZ this ordeal caused him and his wife emotional distress and professional setbacks ... made worse by the soured relationship with a man he considered a brother.

He adds, "But it’s been three years since Kevin promised to help clear my name, to no avail. So here we are. Through this lawsuit, I aim to restore my reputation, seek accountability, and ensure that such injustices do not happen to others.”