Yes you can e-file a return for a minor child. It is not necessary to mail in a return but if you do mail in a return, the minor will sign his own return.
Please remember:
IF somebody else CAN claim him as a dependent, he is not allowed to claim his own exemption. If he has sufficient income (usually more than $6350), he can & should still file taxes; he just doesn’t get his own $4050 exemption (deduction). In TurboTax, he indicates that somebody else can claim him as a dependent, at the personal information section.
Even if he had less, he is allowed to file if he needs to get back income tax withholding. He cannot get back social security or Medicare tax withholding.
Please review the following Turbo Tax FAQ for more information.
https://ttlc.intuit.com/replies/4790655