@phoenix31775co If the children are living with you, it seems odd that your "ex" is claiming them for all of the child-related credits. Do you have any income from working? Is there some reason you do not want to file as Head of Household, and/or be eligible to get earned income credit or the childcare credit?
But to answer the question you asked, if the ex is claiming them and you are not claiming anything at all, then you do not enter anything about the children on your own tax return.
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