Barrino has appeared publicly with a tattoo on her left shoulder reading "Cook," an apparent tribute to Antwaun Cook, who is said to have a similar tattoo in the same place on his shoulder, according to the documents.
The alleged affair was first reported in November by gossip magazines and websites.
"As [Paula Cook] contemplated ways to save her marriage and family, [Antwaun Cook] and Ms.
Barrino continued to enjoy their open and notorious relationship without her knowledge and/or consent," the documents say.
Barrino and her record label Sony Music declined to comment on the documents Sunday.
Paula Cook says that as a result of the affair, her husband became more and more withdrawn from their marriage, attributing late nights and other absences to work, the documents say.
(CNN) -- A North Carolina woman is alleging that "American Idol" winner Fantasia Barrino engaged in an affair with her husband, and says in court documents that the pair "recorded" their sexual encounters.
Paula Cook, who separated from her husband, Antwaun Cook, in June, filed the documents -- seeking child custody, alimony and other monetary support -- Wednesday in Mecklenburg County District Court.