Legal Question in Real Estate Law in California

You are mixing up legal issues and terms. California law recognizes mortgages, but no one really uses them. The security instrument of choice in California is a deed of trust. The deed of trust is what provides the lender security for the loan which is evidenced by a promissory note.

You don't add a person to a deed of trust. The lender requires all parties who have title to the property that is going to be the subject of the security arrangement to sign the deed of trust. But if your son is not on title in any way, the bank is not going to have him sign a deed of trust.

I'm not sure what you are specifically looking to do, but I do suggest you speak to a competent real estate attorney in depth to get the specific answers you seek.