Dear Aman,
As you know, Pundit supports authentication via OpenID only. The Open Id workflow is initiated the first time you call one of the authenticated APIs (e.g. /notebooks/current) and it is done only once. Subsequent calls are handled by the server locally. Now I'm not an expert in this specific kind of issues. I first would like to understand if I'm getting it right:
Wikidata currently implements a OAuth API for authentication (not authorization). Right? Is it a OAuth 2.0?
What do we want to do exactly, from a users view point?
We want WikiData to be listed among the other identity providers (e.g. Google, Yahoo!, etc?)? Or rather we want a specialized version of Pundit where the only identity provider is WikiData?
What is your idea Aman? Do you want to modify the Pundit Server code (where the OpenId is implemented), and perhaps deploy an other server that supports OAuth? Or you think about adding OAuth as an alternative to OpenId (probably best)? I think this would be non trivial work...
Or you think the behaviour can be enabled somehow working on client side and combining Oauth with OpenId in some way?