Papers filed earlier by Prince's sister, Tyka Nelson, said he had no known children and listed her and five half-siblings as Prince's only known heirs.
The judge overseeing the estate case authorised genetic testing on a sample of Prince's blood in case it's necessary to determine who's entitled to share in his estate, and gave creditors four months to file claims.
Already, a Kansas City woman who says she's Prince's half-sister has come forward, as well as a California man who contends Prince gave him control over his music catalogue and vault via a verbal agreement in the mid-1990s.
The experience of other celebrity estate cases suggests more claims against Prince's estate are likely, and they may not all be legitimate. The court overseeing Michael Jackson's estate case rejected more than US$50 million of dubious claims.
Prince died on April 21 at his home in the Minneapolis suburb of Chanhassen. The cause remains under investigation.
"All we're asking is the truth in this matter," said Williams' attorney, Patrick Cousins, who also confirmed that his client is currently imprisoned.
In her affidavit, Henson said she met Prince in the lobby of a Kansas City hotel and that they later had unprotected sex at a different hotel, at which time she got pregnant.
She said she wasn't married at the time and that she hadn't had sex with anyone in the six weeks before and didn't have sex with anyone else until after she gave birth to Williams.
Court and prison records show Williams is being held at the maximum security federal prison in Florence, Colorado, after pleading guilty in 2013 to unlawfully transporting a firearm. He was sentenced to seven years and eight months.
Henson declined to comment, and Nelson's attorneys did not immediately respond to a request for comment. It wasn't immediately clear when the court might rule. No new hearings are scheduled in the estate case.
Cousins, who represented Prince in the mid-2000s, said they would have preferred to resolve the paternity question privately but the high profile of the estate case made that hard.