“This is a serial number for a product that has been refurbished”

If you believe the information shown for your product is incorrect, you can submit your proof of purchase online

Your sales receipt is needed for Apple’s Limited Warranty, AppleCare Protection Plan, and AppleCare+ validation, so be sure to keep it in a safe place. Apple’s Limited Warranty is the same whether or not you register.

For what device are you entering the serial number? Do you still have that device or has it been replaced, as suggested by the message?

Did you try Settings > General > About > Limited Warranty (or similar)?

Did you purchase it new?

It seems to me there is an issue and you should consider trying to cancel the purchase.