Setup Custom connector as web based application

[Mohanasudharsan]

We are developing a web-based application for our database. We want to create a custom connector for Power BI to load data from the database using the web-based application.
We want to develop an m query to authenticate like the below image when clicking on sign in option it will go our web application in the default browser and authenticate. 

Can someone help us with the authentication setup code sample in m query language, since this is new to us?
We tried web.contents, web.browsercontents not so sure about this connector topic.