Unfortunately, there is not an additional deduction for your son.
You will receive a $500 Credit for Other Dependents as long as your Adjusted gross income (AGI) is not over $200,000 (400,000 if Married Filing Jointly). Depending on your AGI, your son may also be a qualifying child for the Earned Income Tax Credit.
Please see this TurboTax Help Article for additional information: Why am I getting the Credit for Other Depends instead of the Child Tax Credit?