I have a house and live in Long Island. Also I rent an apartment in New York City where my children live.

I pay for the apartment rent and utilities with my checks, and children give me money back.

Now I have an audit, and auditor says that if I maintain apartment in the city I am a NYC resident and should pay NYC resident tax.

Any comments about this would be greatly appreciated.

Unfortunately, that IS what the NY tax law says, and, given the fact that the rent and utilities are being paid by your check, it seems pretty clear that you have in fact maintained an apartment in NY City.

Unless you can clearly show that the apartment in, in fact, in your children's name, you will have a REAL difficult time proving to the auditor's satisfaction that you are not a NYC resident.