Josh Duggar: I'm Not Letting That Porn Star Drop Her Case

The porn star who sued Josh Duggar for allegedly roughing her up during a sexual encounter wants to drop the case ... but Josh is not willing to let it go that easily.

Danica Dillon wants to dismiss her lawsuit, but there's a catch. She wants the option to refile at some point in the future ... this according to new legal docs.

Here's her problem. Under the law she lost her right to simply drop the case with an option to refile. Dillon says in the docs her lawyers approached Josh's attorneys to see if they'd be agreeable to the dismissal, but they balked.

Josh's lawyers say they'll only agree if Dillon drops her case forever and retracts her allegations on her social media accounts. He also wants her to foot his legal bills.

She's refusing Josh's offer, and adds in the docs he might think twice before digging his heels in, because of his admission he's been treated for sex addiction.

As TMZ first reported, Duggar claims he never had sex with Dillon and has an alibi to prove it.