To sleep. I'm not sure of how many ways to use it though.
If you were sleeping you wouldn't be "z'ing."
The only way I know how, or have heard anyone use it is in the example.

Intelligence agency term for "psychological operation". A government or corporate-sponsored operation, usually taking the form of a "terrorist attack" or "crazed gunman on a spree", with the intent of panicking the public into demanding more police and laws inhibiting freedom. Psyops are usually carried out by drugging a civilian or group of civilians with aggression-promoting drugs, psyching them up, arming them, and sending them out to commit mayhem. Government-sponsored terrorism. See also blackshirts, conspiracy

When a young (Usually black male) sells Ounces of Cocaine in a Reanault Clio in North london

To put "Zs" on somebody means to knock them out or beat them in a fight by putting them to sleep.