How to connect to aws-api-gateway websocket?

I need to create a full duplex connection between arduino and my website. How do I connect arduino to my aws-api-gateway websocket?

I have already worked on Markus Sattler websockets library,it works fine on local network, but I don't know if its possible to connect that library to aws-api-gateway socket or there is some other library to do so.

All I need is a continuous connection between website and arduino where data is sent from arduino to database(dynamodb) via lambda function and arduino listening every message sent from website to it. Here is url to the websocket: