Green’s Dictionary of Slang

(US drugs) a quarter pound of cannabis; note def. in cit. 2002 is probably an error.

2002		Danktuary Marijuana and Mushroom Dict. 🌐 QP [n.] One quarter ounce [sic] of pot.
2004		A. Mansbach ‘Crown Heist’ in Brooklyn Noir 126: He came by at night, picked up a QP.
2015		Chief Keef ‘Macaroni Time’ 🎵 I gotta QP of Earth rolling, let's get high.
2019		N. Walker Cherry 248: [W]e averaged $4500/lb selling it [i.e. homegrown marijuana] off in QPs and ounces.