Simple answer: No.
The money you hear about people getting for just filing a
tax return claiming kids requires you to
have some earned income (wages or self employment). Without earned
income, you are not eligible for the "refundable" Earned Income
Credit or Additional Child Tax Credit.
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)
For tax purposes, a child is the
"Qualifying Child" of any close relative he lives with. not just his
parent. For example, if you and your children live with your parents, you can
allow them to claim your child, instead of you.