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.
If you are a student, over age 23, or married, 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. There's even a loop hole available to claim the credit, if you are on scholarship (read on for an explanation). If your "financial aid" is loans, it is not necessary to use the "loop hole".
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There is a tax “loop hole” available to claim an education credit, for the parents (or the student himself) of students on scholarship. The student reports all his scholarship, up to the amount needed to claim the American Opportunity Credit (AOC), as income on his return. That way, the parents (or herself, if she is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship. You cannot do this if the conditions (restrictions) of the scholarship are that it be used to pay for qualified expenses. Pell grants are not restricted.
Using an example: Student has $10,000 in box 5 of the 1098-T and $8000 in box 1. At first glance he/she has $2000 of taxable income and nobody can claim the American opportunity credit. But if she reports $6000 as income on her return, the parents can claim $4000 of qualified expenses on their return.
Books and computers are also qualifying expenses for the AOC. So, extending the example, the student had another $1000 in expenses for those course materials, paid out of pocket, she would only need to report $5000 of taxable scholarship income, instead of $6000.
If you have no other income, the amount of "taxable scholarship" you report will not be enough to actually generate any tax.
