You are not required to file. This assumes you have no other reportable income. And there's no benefit to filing. 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.
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.
If you were 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)
