The 29-year-old basketball star - who has a two-year-old daughter called True with Khloe Kardashian - has decided to take legal action against Kimberly Alexander for libel.
Tristan has also demanded a jury trial against Alexander, according to E! News.
The sportsman - who split from Khloe in early 2019, after he was involved in a cheating scandal with Jordyn Woods - recently threatened to take legal action against Alexander in a cease and desist letter.
The document urged her to "immediately stop defaming [Tristan and Khloe] with malicious defamatory lies and specious fabrications".
And in the new court documents, Marty Singer, Tristan's attorney, alleges that the defendant is a "wannabe social media influencer and pornographic model/performer who is so desperate to achieve her fifteen minutes of fame that she recently fabricated a false claim that NBA star/Cleveland Cavaliers centre/power forward Thompson is the father of her nearly five-year-old son".
What's more, the court documents explain that Tristan "voluntarily" submitted a DNA test to "definitely determine the child's paternity" - even though he didn't think he was the father of the child.
One passage of the document reads: "Alexander has persisted in publicly proclaiming that Thompson is her child's father and she has maliciously accused Thompson of being a deadbeat dad, 'neglecting' and failing to take financial responsibility for the child since birth.
"Such statements are absolutely false and are defamatory per se. To quote Michael Jackson, 'the kid is not [his] son'."
Tristan's attorney said that, rather than accepting the scientific results, Alexander has instead accused the lab of "trying to sabotage a DNA test" with the basketball star.