Q: How client will handle the connection in case of failure of IP of HA proxy I have setup a postgresql cluster (with one master node and one slave/standby node) using Patroni. I want to use HA proxy in front of my cluster. 
I think in this case HA proxy itself could be a single point of failure. 
So to avoid this problem if I use multiple nodes for the HA proxy. Then not sure how client will handle the connection in case of failure of IP of HA proxy to which client is corrently connected.
( Or we can say how client/client_app will switch over between different available IP's of HA proxy).

A: For the client/application itself, that depends on your implementation.
Basically, it's your responsibility to handle connection errors (e.g. severed/dropped) and do as you will -- such as re-connect.
You can use something like keepalived to handle IP fail over from HAProxy A to B.

A: I think the question is what would happen to the client connection in the HA setup with multiple haproxy when the haproxy instance the client connects to goes down.
In the best case scenario, your client will get an error and reconnect to the next available instance. You can round-robin your haproxy instances via the DNS, or use the floating up to switch between them, or cascade the haproxy, setting the application-facing instance on the same host as the application itself. In any case, if your haproxy instance is down - your connections will terminate. There is no way around it.
