If your son can be claimed as a dependent (by you or anyone else) he is not eligible to get any stimulus payment of his own. It doesn't matter whether you actually claim him or not. If he can be claimed as a dependent he is not eligible for any stimulus payments.
If you claim him as a dependent on your tax return you will get an additional amount for your dependent for the third stimulus payment. For the first two stimulus payments you cannot get a payment for him as a dependent because he is over 16 years old.
