Green’s Dictionary of Slang

q n.

[abbr.]

1. (US) a male homosexual [queer n. (6)].

[US]Guild Dict. Homosexual Terms 38: q. cards (n.): Gay (homosexual) calling cards; usually with the addition of symbols or phrases below the name. As distinguished from gay notepaper.
[US]Baker et al. CUSS.
[US]B. Rodgers Queens’ Vernacular.
[UK]Kirk & Madsen After The Ball 258: ‘Q-types’ – homosexuals on display. Q’s don’t wish to be seen as straight.

2. (UK drugs) a quarter ounce of a given drug.

[UK]N. Barlay Curvy Lovebox 45: How many was you wantin’? Ten . . . and a q.
[UK]Guardian 11 July 6: The police are not going to lift you at a party for having a half Q [eighth of an ounce] just now, so what difference will this make?
67 ‘Hashtag’ 🎵 Tryna get Ps from Qs and Os.
[UK]G. Krauze What They Was 13: We can buy a draw or two [...] or maybe a q [and] get properly faded.

In phrases

on the Q (adv.)

(US) surreptitiously, on the quiet.

[US]Brooklyn Dly Eagle (NY) 11 Dec. 4/7: ‘The Ballad of the Bunco man’ He was a festive bunco sharp / And had a little plan / For catching shekels on the Q / From the verdant countryman.