Theodore Deland's “Sphinx Card Trick,” 1909, may be the first example of this effect. The earliest ad for it seems to be by W. D. Leroy and appears in The Sphinx, Vol. 8 No. 5, July 1909, p. 97. Ellis Stanyon advertised it in Magic, Vol. 9 No. 12, Sep. 1909, p. 91. In both ads, it is clearly stated to be DeLand's trick. Curiously, you can find a brief description of it in Karl Fulves's Ellis Stanyon's Best Card Tricks, 1999, p. 132. Three cards were placed in a hat and one removed and put into the deck. When the hat was next checked, it contained the one card seen removed, and the other two were found in the deck. Misprinted gaffs were used. A variant, “The Renovated Sphinx Card Trick,” was contributed by Eddie Clever to The Jinx, No. 9, June 1935, p. 34.
Ken Beale is reported to have proposed an asymmetric card transposition in 1967, using four Kings and two Queens; and Persi Diaconis worked out a method around this time. Neither Beale nor Diaconis have published their methods. The first to have published a non-gimmicked method seems to be Karl Fulves; see “Four Gone,” in his Notes from Underground, 1973, p. 53. Shortly after that, Peter Kane published a version, “Diamond Robbery”, in A Further Card Session with Peter Kane, 1975, p. 2.
Johann Nepomuk Hofzinser had an effect “Drei ist Eins” (“Three is One”), which was mentioned in passing without details in Ottokar Fischer's book J. N. Hofzinser Kartenkünste, 1910, p. 215. The whole effect was finally published by Magic Christian in his J. N. Hofzinser: Non Plus Ultra, Vol. II, , 2004, p. 192. In this effect, a chosen card is placed aside. Then three unknown cards are taken from the deck. One by one they are shown to be duplicates of the selection. Then all three are placed on top of the deck. The chosen card is turned over and is seen to consist not of one, but three indifferent cards. On top of the deck, the selection is found. While this effect has the elements of an asymmetric transposition, this aspect is not clearly worked out as the three cards are never shown at the beginning.