Green’s Dictionary of Slang

amjay n.

[backsl. jam n.1 (2a)]

(US) a problem.

[US]J. Woods ‘Sports Topics’ in Brooklyn Dly Times 27 Oct. 2/1: [T]he Boston boy may find himwself in a jam or ‘amjay’ as they say on the curbstones of the lane of Laughs and Lights.