I am an F-1 student in GA since 2020. From 05/20/2024, I moved in TX for an internship until 12/20/2024.Do I owe state taxes to GA for the income in TX?

@mikoKoko7 , thank you for your response(s).

So you are saying that you entered  this country in Jan  of 2020 with F-1 ( and with NO earlier entries to consider ).  That says your  Exempt status is quenched on 12/31/2024.    So why do you say that your counting of presence started Jan 1st of 2024 , thus giving a SPT passing around Jul of 2024.  Please , I am missing something here.   

Were you present in the USA prior to calendar year 2020 ?

The exempt period is FIVE Calendar years from the year of entry -- so whether you entered with F-1  in   Jan  ( ??) or Sept.  (usual ) of the calendar year 2020, your exempt period  ( barring a  status change )  still ends on 12/31/2024.

If this is correct, then for 2024 you are still a NRA and must file form 1040-NR ( not supported by TurboTax ).

Your other question  of whether  you need to pay taxes to GA  ( your  resident state ) on income earned in TX,  would generally be YES.  Most states  tax you on world income and generally give you credit for taxes paid to another US state  ( except  for  states with reciprocal agreement).