Your refund is not broken down by how much you "get" for each dependent.
There are several child-related credits you *may* get if you have a dependent child and if you have income earned from working.The amount earned by working has a major effect on how much you receive for the child-related credits.
You might be getting the Child Tax Credit--that is not all a refund--it lowers the tax you owe, up to $2000 per child, but if you do not owe tax then you may not get the full amount of CTC. In some cases, you could qualify for the "Additional Child Tax Credit" which is a refundable credit, and would increase your refund. If you qualify for this credit, TurboTax calculates and automatically adds it to your refund.
You might be able to claim the child and dependent care credit if you paid someone to take care of your child so you could work. This is not a refundable credit, so it will not be in your refund. It can lower the tax you owe.
You might qualify for Earned Income Credit, which is a refundable credit if you worked and earned income. The EIC is based on the amount you earned. If you do qualify for EIC, TurboTax automatically calculates the amount and adds it to your refund.
Look at your 2020 Form 1040 to see the child-related credits you received
Child Tax Credit line 19
Credit for Other Dependents line 19
Earned Income Credit line 27
Additional Child Tax Credit line 28
Child and Dependent Care Credit line 31 (from line 13 of Schedule 3)
And in addition to the child-related credits you can get stimulus money for your child. Make sure you go through the screen for the recovery rebate credit.
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, 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.