Hi, what is the status of a refugee or an asylum case, with work permit and a licence drive. Is he an alien resident or an alien non resident?

In order to be considered an Alien Resident, you must either meet the Green Card Test or Substantial Presence Test for 2022.  If you do not meet the criteria listed in the links to be considered an alien resident, then you would be a non-resident alien.  

If you are a non-resident alien, you would need to file form 1040-NR which TurboTax does not handle.  However, you can file this form with Sprintax.com as that is what they specialize in.