Can I gift stock to my child?

Yes, you can gift stock to your child. Earlier to transfer the shares as a gift to your child for their future development, you can do it using your physical shares certificate. After 2019, the transfer process through physical shares certificate was made unpracticable.
Now it is only possible to transfer your shares to your child only through demat account. If you have physical share certificates, you have to convert them into Demat and then you can transfer shares as a gift to your child. For this your child should also have Demat account.