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William Shatner is being sued for $170 million by a radio host who claims to be the “Star Trek” legend’s long-lost son.

Peter Sloan has boldly gone and filed legal paperwork in Florida demanding Shatner submit to a DNA test and cease claiming he isn’t his father.

Sloan, 59, claims his birth mother, late Canadian actress Kathy McNeil, had a brief affair with Captain Kirk in Toronto. She gave him up for adoption at 5 days old.

But Shatner, 85, denies Sloan is his son, and claims the local radio host is trying to unfairly live long and prosper from the connection.

In the lawsuit, filed in Tampa, Fla., Sloan states he met with the actor on the set of “T.J. Hooker” in 1984 and Shatner initially “admitted he was the plaintiff’s father.” But a week later, Sloan claims, he was contacted by a rep for Shatner, who said he was “totally denying paternity at this point,” and added, “Don’t go public . . . [as it] could be horrendous for [Shatner],” who refused a DNA test.

After Sloan surprised Shatner at a meet-and-greet, registered the Web domain petershatner.com and began a local CBS radio show in 2011 under the name Peter Shatner, he got a letter from Shatner’s lawyer, Erik Hyman, saying his actions were highly illogical.

“Bill . . . confirmed to me once again that he is not your father. There have been many people over the years who have claimed to be his children or other relatives,” Hyman wrote, adding, “He is an incredibly busy, 80-year-old man, and is not interested in spending time discussing this issue with you.” Hyman didn’t comment last night.

Sloan alleges in the papers that reps for Shatner had succeeded in getting Twitter to shut down his feed, and IMDb Pro to take down a page about a movie he was working on.

Sloan — who wants to beam up to a jury trial — told us, “I am William Shatner’s son, and I just wish he would acknowledge me.”

Shatner’s rep told us, “Mr. Shatner has three lovely daughters, but no sons . . . Mr. Shatner is aware of the lawsuit, but there’s nothing there because he isn’t his father.”