A shortening from Abraham. In the slang sense for money, refers to the picture of Abraham Lincoln on the currency.
Meanings
(US, slang) A five-dollar bill.
"Gambling's not my form of masochism," said Carl. "Huh?" "So how much?" "The wad's mostly ones. Some Jeffersons. Two or three Abes." 1996, J. Madison Davis, And the Angels Sing, page 210: