The Three Jacks Deal, in which three Jacks are placed on top and repeatedly dealt into one player's hand in a two-handed game despite a fair alternate deal, was published without attribution in Rufus Steele's Card Tricks You Will Do, 1928, p. 20, as “Jack - Jack - Jack”.
In The New Magician’s Manual, 1936, p. 56, Walter Gibson published “The Poker Deal”, which is an elaborated multi-phase routine based on the Three Jacks Deal principle, accompanied with a story presentation. Harry Lorayne made his handling of Gibson's routine popular under the title “Big Fella, Little Fella” in Close-up Card Magic, 1962, p. 61.
For research on this plot see Jon Racherbaumer's Provenance Bulletin 1-5, 1997, p. 4, “Provenance Bulletin 3: Three Jacks Deal”.
The central principle of the Three Jacks Deal is shared with the trick of placing one of three Knights on top of the deck, another on the bottom and the third in the middle, after which the deck is given a cut and the three Knights are shown gathered together in the middle with a Queen. This trick goes back to at least the 1700s (e.g., see Pablo Minguet's Engaños a ojo vistas, 1733, p. 168 of the Pieper translation; the translation appeared in Gibecière, Vol. 4 No. 2, Summer 2009, pp. 61-225) and is a likely seed for the development of the Three Jacks Deal.