Yes. A child dependent has to file a return if their unearned income exceeds $1,050. Capital gain is unearned income. He may be subject to the "kiddie tax", but all of the calculations will be handled in TurboTax.
It's possible you may be able to choose to add the income to your return for your child. However the tax rate may be higher on your return. If you claim him as a dependent he must select that he is being claimed by someone else.
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In TurboTax Deluxe: Federal Taxes > Wages & Income > Investment Income > Stocks, mutual funds, bonds, other
Depending on the child's total unearned income amount, and on your tax bracket, you may be able to elect to report the child's unearned income on Form 8814 inside of your return. See here for requirements and detail: Tax on Child's Unearned Income - IRS Topic 553
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In TurboTax Deluxe: In your return this is found under Wages & Income, Less Common Income, "Child's Income (Under Age 24)".
The information provided below will give additional details.
https://ttlc.intuit.com/replies/3301446
