I work in NY, but live and rented apartments both in NJ and NY. I only stay in NY tue-thursday but stays with my family in NJ fri-monday .which address is appropriate in filling "MARRIED FILLING JOINTLY" status? Ny or nj address

I would *guess* that you would file where your family lives. This would be considered your primary residence.

When you file, use your NJ address.

However, for your NY return, the state of NY and especially NY City will consider you to be a NYC resident if you maintain an apartment in the city.

What is the address on your driver's license? Where are you registered to vote? What is the address on file with your employer? These would indicate your primary residence.

The address with my employer is my NY address. But my family reside in my NJ rented apartment.Can I file with my NJ address for my federal tax return(married filling jointly status) and fle with my NY address for NY state resident tax return?Can I claim a different state address for the federal and the state tax return?

1. You must give same address on NY and NJ tax return. On NY return you can give NJ address. And as Atlanta Tax Expert said: However, for your NY return, the state of NY and especially NY City will consider you to be a NYC resident if you maintain an apartment in the city.
2. You must report your NY income on NY tax retrun.
3. If you are resident of NJ, then you will also report this income on NJ tax return. On NJ tax return, you will claim credit for taxes paid to NJ. If you are not a resident of NJ, then you do not file NJ tax return if you do not have any income from NJ source.