(CNN) William Shatner is being sued for $170 million by a Florida-based radio host who claims that the "Star Trek" actor is his father.

Peter Sloan, who now goes by the name Peter Shatner, says the actor had an affair with his birth mother, Katherine Burt (later Kathy McNeil), in 1956.

Shatner denies that Sloan is his son.

Sloan, 59, was given up for adoption shortly after his birth. In 1984, he started seeking his birth parents and identified the people he believed to be his mother and father.

"Over the months that followed through a process of research and verification, Peter was able to identify his birth father as Canadian born William Shatner," according to petershatner.com , a website registered by Sloan.

The lawsuit (PDF) states that Sloan met Shatner in November 1984 on the set of his TV series "T.J. Hooker." At the meeting, the lawsuit says, Shatner "admitted" he was Sloan's father, but when Sloan followed up with a phone call days later, Shatner "became agitated and hung-up the phone."

A representative for Shatner called Sloan back and told him Shatner "is totally denying paternity at this point." Sloan suggested a DNA test but was "rebuffed," the suit says.

Sloan established petershatner.com in 2009 and started a radio show in the Tampa area as "Peter Shatner."

An attorney for William Shatner then contacted Sloan and told him that Shatner had "confirmed to me once again that he is not your father."

Sloan alleges that Shatner's social media director posted "malicious, libelous and slanderous statements about the Plaintiff (Sloan) on Facebook and Twitter." He also says Twitter and IMDBPro have shut down accounts related to him.

Sloan is seeking $30 million in compensatory damages, $90 million in punitive damages and $50 million for pain and suffering. He is also demanding a jury trial.

CNN has reached out to Shatner's representatives for comment.