Okay---you were asking about state exemptions---that is different. Some states do have personal exemptions. Thought you were asking about your federal return since your question did not mention the state.
If you claimed the children on your NY return, then you are the one who has the "exemptions" for them.
I am confused by your question about what to put on your spouse's return. Are you preparing his return for him---although you live apart?
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