Q : …create additional ZeroMQ socket on each accepted connection for pushing messages from server?
The best trivial composition-based design - both scaling-wise and security-wise
The native ZeroMQ primitives ( the smart primitive Scalable Formal Communications Pattern Archetypes ) are like a LEGO building-blocks for us - we compose their further use on the Messaging/Signalling Plane of the intended target use in our application-domain.
Q : Could you please advice of which ZeroMQ socket type to google for such architecture?
No, given no detailed requirements list was available for such an advice. A pair of PUSH/PULL-s need not suffice on their own, temporarily conducted ( episodic ) REQ/REP may help for the client-(re-)discovery phases, as might other co-existent, persistent or episodic Archetypes do for composing any additional System/Service-Planes.