Claim a child

Well, if you have not worked for the entire year then you would Not be eligible for any type of tax credit based on earned income, such as the Child Tax Credit or EIC.  So with no income there is no need to file a tax return.

He can file a tax return and claim the child on his tax return as a dependent and based on his income and filing status may be eligible for the Child Tax Credit and EIC.  And he may be able to claim you as a dependent under the Qualifying Relative rules and be eligible for the Other Dependent tax credit.

To be a Qualifying Relative -

1. The person cannot be your qualifying child or the qualifying child of any other taxpayer. A child is not the qualifying child of any other taxpayer if the child's parent (or any other person for whom the child is defined as a qualifying child) is not required to file an income tax return or files an income tax return only to get a refund on income tax withheld.
2. The person either (a) must be related to you or (b) must live with you all year as a member of your household.
3. The person's gross income for the year must be less than $4,200 (social security does not count) in 2019
4. You must provide more than half of the person's total support for the year.
5. The person must be a U.S. citizen or a U.S., Canada, or Mexico resident for some part of the year.
6. The person must not file a joint return with their spouse.

If you have no income than you do not even need to file at all and you have not paid any tax to get back.  You get nothing for just claiming  child unless you have taxable income.