Is issuance of Credit Note and Debit Note a two way process?

I am working for a state PSU and it is liable for deducting TDS on GST  @ 2% and the remaining 16% is released to the supplier.

It has come to our notice that in one of the tax invoices excess quantity of an item was supplied and billed which was not in accordance with the contract of supply and as such we have requested the supplier to issue a Credit Note for the excess quantity supplied.

Now, in this situation, I want clarification if I am required to issue a corresponding Debit Note for the Credit Note to be issued by the supplier and is it a two-way procedure to be followed by both supplier and recipient.