when does james discover he is half jewish?

In writing the book, James McBride discovered his mixed ancestry, including his Jewish roots in Virginia. He described the difficulties of acknowledging his whiteness given his "Black" physical appearance. As McBride notes, "being mixed is like a tingling feeling that you have in your nose just before you sneeze -- you're waiting for it to happen but it never does. I believe James was a teenager when he finds out his identity.

He is a teenager when he discovers his mother was Jewish, but there is no such thing as half Jewish you either are or you aren't. It's a religion,i.e. nobody is half Christian or half Buddhist.