Closest thing I’ve found is How to incorporate WebSockets into a Cocoa application, but the answers only pointed to an outdated library.
Does anyone know about a WebSockets library compatible with iOS 4.x?
I’ve also read about Pusherapp, and, as good as the service could be, I would prefer to use my own WebSockets server.
You can check out the UnitT Web Socket Client. It is intended for use in iOS apps using Objective-C. It works with both ws & wss.
I am the author and have been using it in some of my projects with success. Let me know if you run into any trouble and I will do what I can to help.