apple pencil

Your Apple Pencil serial number can be found, when paired with iPad, in iPad Settings:

Settings > General > About - scroll down the list until you find the entry for the Apple Pencil, then tap.

Your Apple Pencil is warranted against manufacturing defects for one year from its original purchase date as described here.

Apple One (1) Year Limited Warranty – Accessory - For Apple and Beats Branded Products Only.