There is a very persistent story that Thomas Jefferson personally executed someone on the White House lawn for treason; some sites name the prisoner as a Rodney Cox from North Carolina. We have no evidence that this event ever occurred: no such thing is ever mentioned in Jefferson's papers, or 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. Several actual events could have been (severely) misunderstood or mistaken for a "Jefferson execution:"
Jefferson was involved in drafting a "Bill to Attaint Josiah Philips and Others" in 1778, which ordered the trial and provided for the execution of the murderer and bandit Josiah Philips for treason. Josiah Philips was eventually found and convicted of robbery, not treason.
The murder of Alexander Hamilton by Aaron Burr in their famous 1804 duel has also been suggested as a possible source for the story in question.
Neither of the above seems very plausible as a source. Unless further reliable evidence surfaces, we can only explain this story as a complete fabrication by the scriptwriters of Swordfish.