Now, why is he not a resident if he's a GCH?  And why do you think only citizens would be eligible?  That's not what §32 says.

Also, is his child a qualifying child for EITC purposes?

You may like to bookmark this helpful IRS webpage for EITC: https://www.irs.gov/credits-deductions/individuals/earned-income-tax-credit-eitc

Edit: The OP has changed the key facts presented in her post.  The response here may not address the OP's question specifically but is still relevant to EITC in general.