You should not claim your child's W-2 or self-employment income on your return even if you claim him as a dependent.
Your dependent may not be required to file his/her own return, but may elect to do so to obtain a refund of his withholding(s).
He can walk through this tool: https://www.irs.gov/uac/do-i-need-to-file-a-tax-return to determine if he is required to file
If the dependent files his own return with TurboTax, he should check the box Someone else can claim me on their tax return in the personal information section.
To enter his W-2 on his own return:
Type in w2 in the search box, top right of your screen, then click the magnifying glass
Click the jump to w2 link in the search results.
Follow the onscreen instructions to enter