Does square support Co-badged cards compliance required by EU?
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Yes, Square supports co-badged cards. Co-badged cards are payment cards issued in the European Economic Area (EEA) that have two or more payment brands. When a buyer makes a payment with a co-badged card, they can choose which payment application to use. Square’s point of sale applications and APIs are designed to comply with the co-badging choice requirements set by the European Union.
This answer was reviewed by @Bryan-Square.
thanks! @Bryan-Square One more question - Do we need to do any changes on our side or everything will be taken care by Square web-payment-sdk or API?
No changes needed on your end. All is taken care of by the Web Payments SDK and the Payments API. 
thank you @Bryan-Square !