If your children do not have a SSN or ITIN, you can choose to leave them off of your return, or you can apply for an extension of time to file your return and apply for an ITIN for your dependents.
Depending on your tax situation, and the age, student status and income of your children, although you would not qualify for the Child Tax Credit, you may be able to claim the $500 Non-Refundable Other Dependent Credit by including them on your return.
US. Tax Guide for Aliens
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