while the post is confusing, I think what you are saying is the IRS denied your child tax credit on your tax return, so that what you owed increased by $500.
Non-resident aliens are not eligble for the child tax credit nor are they eligible for the 'other dependent' tax credit (which I think what was really denied since it was $500)..
As it is a tax credit, and not an income item,. it is unlikely to impact your state tax return.
