In order to make the requests library use a custom ssl context, you need to create a custom HTTPAdapter class and override the init_poolmanager method to pass in extra arguments to the base class's implementation.

See sample code here:

from requests import Session
from requests.adapters import HTTPAdapter
import ssl


class CustomHTTPAdapter(HTTPAdapter):

    def init_poolmanager(self, *args, **kwargs):
        # this creates a default context with secure default settings,
        # which enables server certficiate verification using the
        # system's default CA certificates
        context = ssl.create_default_context()

        # alternatively, you could create your own context manually
        # but this does NOT enable server certificate verification
        # context = ssl.SSLContext(ssl.PROTOCOL_TLSv1)

        super().init_poolmanager(*args, **kwargs, ssl_context=context)


def main():
    client_session = Session()
    client_session.mount("https://", CustomHTTPAdapter())

    # now you can use the client_session to make requests
    # r = client_session.get("https://<web address>/rest/info?f=json")

I solved it using :

requests.post(url,headers=hdr,json={"filterList":[{}]}, cert='myprivate.pem')

A self-signed certificate is a trick to pretend that the CA is the certificate itself. So we have to provide beforehand the client with this certificate in order to trust it when it will be encountered.

In the client, after the creation of the SSL context, I tried something similar to

context.load_verify_locations('/home/hfurmans/ssl-cert-snakeoil.pem')

and it worked.
( https://docs.python.org/3/library/ssl.html#ssl.SSLContext.load_verify_locations)

I only had to remove context.verify_mode = ssl.CERT_REQUIRED in the server because I didn't provide my client with its own certificate, but that was not the problem reported in your question.

Of course, for all of this to work, your certificate must have the correct common-name.
If the client connects to myipaddress (as a hostname), then the common-name of the certificate must be myipaddress too.