QB Issue Resolution:

You will need to enter a Social Security Number for all your employees, whether or not they are US citizens. If you don’t have it right away, and you need to deduct taxes for this employee, you can enter a dummy SSN enter their SSN as soon as possible. However, if you aren’t deducting taxes, you can set your employee as a contractor or vendor. I recommend talking to an accountant if you have any questions about government and accounting requirements, and/or contacting the IRS. You can also look up more information online via government pages, here are a couple links for you:

https://www.irs.gov/businesses/small-businesses-self-employed/hiring-employees
https://www.ssa.gov/pubs/EN-05-10107.pdf

Resolution for Issue 'Can anyone tell me how to enter an employee that is a non citizen national of the USA?' available: Yes (Solved).
Source: Intuit Community forum.

Can anyone tell me how to enter an employee that is a non citizen national of the USA?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

Support for citizen national
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Error Recovery for citizen national [Canada]
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