Do I or my Wife claim our son as a dependent

She gets the CCB payments

You may be able to claim the amount for an eligible dependant if, at any time in the tax year, you met all of the following conditions at once:

You didn't have a spouse or common-law partner or, if you did, you weren't living with, supporting, or being supported by that person
You supported a dependant
You lived with the dependant (in most cases in Canada) in a home you maintained. You can't claim this amount for a person who was only visiting you

In addition, at the time you met the above conditions, the dependant must also have been either:

Your parent or grandparent by blood, marriage, common-law partnership, or adoption
Your child, grandchild, brother, or sister, by blood, marriage, common-law partnership, or adoption and under 18 years of age, or had an impairment in physical or mental functions

It does not matter who among you or your wife claims your son as a dependent.

Let us know if that does not answer your question.