To publish a Costs Credit Note to Xero, change the item’s ‘Type’ to ‘Credit Note/Refund’. This can be done from the Item Details page.
For a ‘Credit Note/Refund’ to be successfully published to Xero, the ‘Publish to’ option must be set to ‘Purchases’. Xero cannot host Credit Notes within the Bank Accounts section.
If you change the destination to ‘Purchases' in the Item Details page then you will be able to successfully publish.
After that you can easily find the credit note in the Accounts >> Purchases >> Drafts section of Xero.
Please note that Sales Credit notes are unable to be published, only Sales Invoices.