In the Dependents section of Turbo Tax, choose Another Person under Who else do you support? The person I support is my: should be answered Other.
Enter the child's information on the next page, Tell us about this person.
On the Tell us a bit more... screen, choose the amount of months the child lived with you.
The following screens determine whether you can claim the child as your Qualifying Relative, which has the same exemption amount as a Qualifying Child.