What do you mean by nonresident children?

Nonresident aliens?

Live with the other parent?

Yes, Nonresident aliens. They don't live with parent as he is in the United States and his children live in Mexico. 

The State return may have an exemption or credit for dependents.

If the taxpayer has a 1095-A for Marketplace insurance the extra dependent increases their Household Size.

Medical expenses are deductible for a dependent.

Offhand, I can't think of anything else.  So in some or many cases, the dependent may not affect the tax return at all.

thanks