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.

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.