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.