Why don’t neither of my children qualify for a tax credit

[SweetieJean]

How old were they on 12/31/2020?

[Hal_Al]

The money you hear about people getting for just filing a tax return claiming kids requires them to  have some earned income (wages or self employment). Without earned income, they are not eligible for the "refundable" Earned Income Credit or Additional Child Tax Credit.  Both credits are calculated on the amount of earned income you have. No earned income means no "refund". A small amount of earned income means a small refund. The child tax credit does not "kick in" unless you have at least $2500 of earned income.

A child can be the “qualifying child” dependent of any close relative in the household. If you live with someone else, e.g. your parents, it may be better if they claim your child.

Instead, you could allow the non-custodial parent to claim the children.  Non-custodial parents are allowed to claim the child tax credit, but not the Earned income credit.