None. Supervisor’s API is not exposed externally. It is only accessible from within the docker network. This is by design, it is not intended to be a public facing API.
If you’re a developer trying to make additions to supervisor then you can temporarily expose its API externally on a dev system by adding the remote API addon. This addon will print you an auth token for supervisor in its logs. Then it will listen on a port on the host and proxy requests made through it to the supervisor API.
But this addon is only for development. It is not an LLAT, the token will change every time it restarts. If you are trying to do this on a production system then consider instead writing your own addon with an auth mechanism that you control and exposing specific functionality you need in an API. That addon can then proxy those requests to the supervisor API.
Although I would be curious to hear your use cases here. I am one of the devs for supervisor. Is it just the ping API for some kind of external healthcheck tool or is there a bigger plan?