Alejandra Jackson -- who has 2 kids by Randy and 2 by his brother Jermaine -- has a child support judgment against Randy that exceeds $600,000 -- that's because Randy hasn't paid his $1,200 a month in years and the debt plus interest swelled into outer space.

Randy has now filed legal docs trying to undo Alejandra's judgment, claiming they cut a deal in 1993 that Randy and Michael Jackson agreed to let Alejandra and her kids live in the Jackson family compound in Encino and in return he wouldn't have to pay child support.

On top of that, Randy says the Jackson family provided Alejandra with food, utilities, maids, cooks, security guards, telephones, gardeners, maintenance, use of numerous expensive cars, etc.

Randy says, in short, she's gotten way more than the $600k he owes her.

Randy also says in the docs, Alejandra and the kids have lived "like kings and queens at Randy Jackson's expense."