Currently, we have the user sign up, and followed by that login is been done in Square. But, I have to implement SSO functionality to consume Square APIs from my application. Could someone please share your thoughts? Thanks.
At this time single sign on isn’t currently available with Square APIs. We’re constantly working to improve our features based on feedback like this, so I’ll be sure to share your request to the API product team. 
Thank you for the input @Bryan-Square! Square APIs can be accessed by passing the OAuth access token which is created from Square. So, for now, to implement a kind of SSO, can I store this access token & refresh token in a storage against the user which will be internally validated by invoking the square Sign-in API. Is the Signup/Login API of Square exposed to an end-user like other APIs?
At this time a Sign-in API isn’t available with our APIs. You can definitely store the access token and refresh token in a storage against a customer but you’ll need to build your own validation since the Square validation of logging in isn’t publicly available.