If you are in Pro plan or Jet plan, manage inventory using serial number products feature will not be accesible for you.
Therefore you can add an additional item custom field to add serial number for your products and show it in the pdf.
Please refer to the article below to add custom item field in the invoice:
If you are looking to manage your inventory using serial number products,
Please refer to the article below to add serial number to your products: Note: This feature is only available in Rise plan