How can I verify the authenticity of my AirPods with serial and model number?

You can’t.

If you have doubts about whether they are authentic Apple products, take them to an Apple Store and have them checked.

Counterfeit Apple products are big business, they fake serial numbers or use a legitimate serial number from a real pair all the time.

Don’t buy products from unreliable sources or people you don’t know or trust.

You don't. If you are interested in buying a legitimate pair of AirPods, the only sure way to do that is to purchase from Apple or Authorized Apple Seller.