Are there any religions that identify with the Abrahamic tradition but aren't part of the big three? Did they fall by the wayside a thousand years ago, or did they only ever catch on in one little corner of the world?
There's also the Yazidis and the Samaritians
The Samaritans are about as Abrahamic as it gets, claiming to have kept the faith while the Israelites who were exiled to Babylon distorted it. There are less than a thousand now. The Yazidis seem less so, having elements of Zoroastrianism and Mesopotamian religion.
The easiest answers are probably the Bahai religion and the Druze religion, both offshoots of Islam. A more interesting corner case is the Mandeans of Iraq; they revere a number of biblical figures(most importantly John the Baptist) but not Abraham and are probably the the only extant Gnostic religious group from antiquity.