Jeremy Renner -- My Wife Extorted Me with Intimate Videos

Jeremy Renner's estranged wife threatened to release intimate videos of him if he ever went back on his promise to help her get a green card ... this according to legal docs Jeremy just filed.

Renner is in the middle of a bitter child custody fight over their nearly 2-year-old daughter Ava. Sonni Pacheco's gunning for primary custody of their child and wants more than $13K a month in child support.

Jeremy has been sharing 50/50 custody since they split up in December.

In Jeremy's new legal docs -- obtained by TMZ -- Jeremy says Sonni repeatedly admitted she married him to get a green card and financial stability. He claims she repeatedly told their roommate Jeremy should be nice to her and not fight her on the green card or money issues or she'd release the embarrassing videos to TMZ ... By the way, TMZ never spoke with her and we wouldn't post such videos.

Jeremy says there are multiple issues of bad parenting on Sonni's part, the worst of which was back in September when he was on location and she left their kid alone in the house for 15 minutes. She went in an Uber to party and never checked to see if someone was at home to care for Ava.

Their roommate filed a declaration saying Sonni smokes and drinks and in fact stopped breast feeding because she felt guilty she was drinking alcohol.

The roommate also claims Sonni did coke during a vacation right after Ava was born.

We've reached out to Sonni's reps, so far no word back.