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6 year oldShe told CBS News a man had approached her in a Las Vegas car park in 2011.
The stranger allegedly said "leave Trump alone", then looked at her young daughter and added: "It'd be a shame if something happened to her mom."
Mr Trump strongly denies having had an affair with the actress.
His lawyers are seeking $20m (£14m) in damages from her, saying she broke a non-disclosure deal signed before the 2016 presidential election. She says the claim is invalid.
Ms Clifford said she had had sex with Mr Trump just once, in a hotel room during a celebrity golf tournament in Lake Tahoe, California, in July 2006. Mr Trump married Melania Trump in 2005.
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