Can I enter the serial numbers for an item in a purchase order?

No, in Zoho Inventory you can enter the serial numbers only in bills and invoices. You can either create a new bill or convert an existing purchase order to a bill. At that time, the Add serial numbers option will become available under the Quantity section for the items that are serial number tracked.

Note: The item will be serial number tracked only if you check the Track serial numbers checkbox at the time of creating the item.