Can attendees login and check their paid or remaining balance when using Square payment?

Using a registration form with payment option (Square), can attendees log in and check their paid or remaining balances?

If so, would this be done through JotForm or Square site? 

I don't think that is possible considering that users do not have the option to create their own account and link their card after the transaction is completed in the form.

You have to inform them about the balance and that you will charge them later on. You can send them an autoresponder email with the details of their partial payment and balance.

https://www.jotform.com/help/26-Creating-a-Form-Autoresponder