I can't verify my AirPods serial number

You're not talking directly to Apple here. We are just fellow Apple-product users, so none of us can send you a replacement pair.

If you have been entering the serial number for these AirPods here:

• Check Your Service and Support Coverage - Apple Support

... and if they show up with a "Invalid Serial Number," then there is a chance that they are fake. However, Target should be an Authorized Apple Reseller, so they should be genuine. Regardless, Apple does not repair them. Instead, you can get replacements, either through Apple or by going back to Target.

Ref: Replace your AirPods - Apple Support

What Apple device are you trying to enter a serial number for? You posted in the Apple networking area that would be for devices, like the AirPort Extreme or Express base stations or the Time Capsules.