Green’s Dictionary of Slang

big time n.2

[SE big + time n.]

(US prison) a lengthy sentence, three years plus.

1939
19401950196019701980
1981
[US]Howsley Argot: Dict. of Und. Sl.
J. Webb Badge (2006) 302: BIG TIME Time served in any state penitentiary.
[US]M. Braly Felony Tank (1962) 18: He didn’t really trust anyone who hadn’t served big time.
[US]P. Thomas Down These Mean Streets (1970) 312: I didn’t know what had happened to Danny and Billy. Maybe the Bronx had them doing some big time.
[US]E.E. Landy Underground Dict. (1972).
[US]E. Bunker Little Boy Blue (1995) 46: You’ll make the big time yet. Just like your brother. You said he’s in San Quentin?

In derivatives

big-timer (n.)

(US prison) one who is serving a long sentence.

[US]C. Shafer ‘Catheads [...] and Cho-Cho Sticks’ in Abernethy Bounty of Texas (1990) 198: big timer, n. – someone doing a long sentence.