An early description, perhaps the first in print, of concealing a coin in edge grip – held parallel to the fingers, between the thumb and length of the fingers – appears in Coin Magic by Jean Hugard, 1935, p. 25, within the description of “Dime and Half Dollar Vanish”. The dime is held broadside to the audience, by its opposite edges between the thumb and first two fingers, concealing the half dollar in edge grip. The edge grip is managed by the thumb and first two fingers (rather than between just the thumb and second finger, as is now most commonly done).
Two years later, in The Strange Inventions of Doctor Ervin, 1937, p. 24, Dariel Fitzkee described the grip, remarking that it “has not heretofore appeared in print to my knowledge. It might be new…” He may have been marginally correct, in that, in his description, the visible coin is held at one side only, pinched between the tips of the thumb and first two fingers, to make the position of the concealing fingers look natural. The concealed coins are held as in the Hugard description, with one edge pressed against the thumb, and the opposite edge pressed against the first and second fingers, possibly clipped narrowly between them (neither the Fitzkee nor the Hugard descriptions and illustrations are clear on this point).
This concealment doesn't seem to have inspired much interest until the early 1970s, when David Roth began fooling magicians with it in such routines as his version of John Ramsay's “Hanging Coins”; see Apocalypse, Vol. 1 No. 6, June 1978, p. 68. The grip Roth popularized moved the one edge of the coin or coins from the first and second fingers to the surface of the second finger alone.