Your post is confusing. You refer to filing with the IRS (Federal) as a "non-resident", but then mention Illinois state. And this is not the Taxact website. It is Turbotax.
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.
My apologies. Let me rephrase.
I filed taxes as non resident alien since I lived in the US for 2 weeks of 2021 and had employment income for those two weeks. IRS owed me $1100 and using that info I filed my IL state taxes but later sent me a notice that now they owe me $1600 since - 'we changed the amount claimed as nonrefundable child tax credit on your tax return since you either didn't enter an amount or entered it incorrectly based on number of boxes you checked on page 1 of your tax return. We changed refundable child tax credit claimed because there was an error on schedule 8812, credits for qualifying children'. To clarify, I have a 3 yr kid who is US citizen and received advance child tax credit last year along with employment income. I provided all relevant information with regards to my tax situation while filing taxes. So now my question is, with this info, do I need to file an amendment for my states (IL) taxes and will that increase the refund amount owed by the state of IL. I was originally given a refund of around $400 for filing state taxes.