There is a persistent story that, on the White House lawn, Thomas Jefferson personally executed a prisoner for treason. Some sources name the victim as a North Carolina man called Rodney Cox. We have no evidence that this "execution" ever occurred; no such event is mentioned in Jefferson's papers, or in contemporary newspaper accounts. The story, as far as we know, originated entirely with the movie Swordfish (2001), where it is mentioned by John Travolta's character, Gabriel Shear.
The true origins of the story are a puzzle. Certain actual events could have been (severely) misunderstood or mistaken for a "Jefferson execution":
Neither of the above events seems very plausible as a possible source for the story in question. Unless reliable evidence surfaces, we can only explain this story as a complete fabrication by the scriptwriters of Swordfish.
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