Over the weekend, Dame took to social media to read docs filed by NYC lambasting Jay-Z for deflating enthusiasm for the auction ... which will sell off Dame's one-third share of the album.

In new docs, the NYC Department of Social Services straight up claimed Jay-Z was "poisoning" the auction through public statements indicating Dame's piece of "Reasonable Doubt" would revert back to Jay in 2031. The City claims that's not how it'll work per the recording deal Jay-Z signed, and insists rights for 'Reasonable' will remain with Roc-A-Fella until 2098.

According to the City, this would mean the winning biding could be 10x higher, because whoever wins could make money off the album for the next 74 years, instead of a mere 7.

The City's Dept. of Social Services has a vested interest in this case because the money Dame makes off the auction will pay off his massive $193,000 child support debt. He also owes the state several million in back taxes.

According to the docs, Jay's ultimately damaged the city's interest in getting the highest possible bid in the auction -- but Roc-A-Fella Records fired back Monday, through attorney Alex Spiro, saying Jay himself never issued any public statements ... and the media simply ran with his termination notice and comments from his "legal team."

RAF now says the issue of whether the termination notice reverts the rights back to Jay-Z is "woefully unripe" -- insisting "this is not the appropriate time, forum, or case" to address these issues.