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I joined USA with H1B visa starting from 15th Feb 2020 whereas my wife joined me on H4 Visa starting from 8th Aug 2020. So in this case I am a Resident alien but what would be the case for my wife? will she be a resident/non-resident alien, because she is on H4 hence won't be eligible for SSN.
In my W-2, I have filling status as "Married Filing Jointly"
Whether your wife has a Social Security Number is irrelevant to whether she is a resident alien. Anyone who passes either the Green Card Test or the Substantial Presence Test is a resident alien. You are a resident alien for all of 2020 because you pass the Substantial Presence Test for 2020. Assuming that your wife has not been in the US in previous years, she does not pass the Substantial Presence Test for 2020, and is therefore by default a nonresident alien for all of 2020. Nonresident aliens cannot file jointly (unless treated as resident), so by default you would have to file as Married Filing Separately.
However, since you are a resident alien, you guys can choose to use the Nonresident Spouse Treated as Resident option, which treats your wife as a resident alien for all of 2020, and requires you guys to file as Married Filing Jointly. Note that being a resident alien means that your wife's worldwide income for the whole year would be subject to US tax, and would need to be reported on your joint tax return, though she may be able to use the Foreign Earned Income Exclusion to exclude US tax on foreign income from the part of the year before she came, and/or use the Foreign Tax Credit to avoid double taxation.
