If you had no income earned from working then there are no child-related credits that you can get by filing a tax return. All of the child-related credits such as earned income credit, childcare credit or child tax credit are based upon working and earning income.
You do not say how you supported yourself and your dependents--it sounds like there could be someone else who supported you and/or your children who might be able to claim you as dependents. Were you supported by someone else?
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.
If you are a student, over age 23, and are not claimed as a dependent by someone else (e.g. your parent) you may be eligible for the up to $1000 refundable American Opportunity (tuition) Credit. That credit is not dependent on having either kids or earned income. You must be at least a half time undergraduate student and actually paid tuition (not just had it paid by grants). Tuition paid by loans counts as paid by you (since you have to pay that back, someday).
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.