On the PAN Card Application form (49A) , Can I sign on my minor child's photograph?

It doesn't really matter, as minor PAN Cards don't have photo. It will say 'Minor' in place of the photo.

For minors to receive a PAN Card, they must submit proof of identity and proof that the parent has provided proof of their address.

Also, the application must be signed by the parent who submitted the documents. The signature of the parent will be printed on the PAN card.

A minor can file for corrections in PAN Card data once they reach 18 years old. They can also submit photos and update their signature with the income tax authorities. The Minor PAN Card will be updated with a photograph and signed.