A lot of variables are part of that.  But all of the child-related credits require that you worked and earned income.  Without income from working --no refund for claiming a child.

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.

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 2019 Form 1040 to see the child-related credits you received

Child Tax Credit line 13a

Credit for Other Dependents line 13a

Earned Income Credit line 18a

Additional Child Tax Credit line 18b

Child and Dependent Care Credit line 18d

https://ttlc.intuit.com/questions/1900923-what-is-the-child-tax-credit

https://ttlc.intuit.com/questions/1900643-what-is-the-child-and-dependent-care-credit

https://ttlc.intuit.com/questions/1899157-what-are-the-qualifications-for-the-earned-income-credit-e...

https://www.irs.gov/credits-deductions/individuals/earned-income-tax-credit/use-the-eitc-assistant

https://ttlc.intuit.com/questions/4499708-what-is-the-500-credit-for-other-dependents-family-tax-cre...

There are no refunds for dependents.  You may or may not be eligible for a Child Tax Credit or Other Dependent Credit but those are included in your tax refund or reduce the amount of taxes owed.