Context
Why this one drifted
The misremembered version is arguably the better standalone sentence — and that is exactly why it spread. Lifted out of the scene, “No. I am your father” is a non-sequitur: no to what? The line only parses as a reply, because Luke has just said Vader killed his father. To quote it on its own, people unconsciously repaired it, swapping the dangling rebuttal for the name of the person being addressed. The misquote is a self-contained sentence; the real line is half of a two-person exchange.
The scene was also built to be hidden, which left the words unusually free to wander. David Prowse, inside the Vader suit, was never given the real dialogue — he spoke placeholder lines, and only Lucas, director Irvin Kershner and Mark Hamill knew the twist. James Earl Jones’s voice was laid in afterwards. The line that lodged in the culture was never performed on set at all.
The misquote is a sentence. The real line is an answer.
The novelization spoiled it first
A curiosity that bears on the “where did it come from” question: Donald F. Glut’s novelization, published by Del Rey on 12 April 1980, reached readers before the film opened on 21 May 1980 — so the revelation was in print before any audience saw it. That does not make the book the line’s origin. The novelization is expressly “based on the screenplay… by Leigh Brackett and Lawrence Kasdan from story by George Lucas” — it is downstream of the script, not upstream of it. Unlike Gone with the Wind, where the film sharpened a line already in Mitchell’s novel, here there is no earlier novel or play to credit.