In general, it is very difficult to obtain immigration relief for a noncitizen convicted of a controlled substances offense.  However, there are some limited forms of relief available.

BIA

CONTROLLED SUBSTANCES - RELIEF - PAULUS DEFENSE INAPPLICABLE
Matter of Martinez-Espinoza, 25 I. & N. Dec. 118 (BIA Nov. 4, 2009) (unidentified substance defense under Ruiz-Vidal v. Gonzales, 473 F.3d 1072 (9th Cir. 2007); Matter of Paulus, 11 I&N Dec. 274 (BIA 1965), inapplicable where burden is on noncitizen to show not ineligible for relief by a preponderance of the evidence). NOTE: This may not be true in the Ninth Circuit. See Sandoval-Lua v. Gonzales, 499 F.3d 1121, 1124 (9th Cir. 2007).