Because he is an adult and because of his mental illness and given that he may lack capacity to give you power of attorney (remember he has to have capacity and want to name you and also sign the document) a guardianship is probably the most appropriate method. You will need to hire an attorney to assist you in obtaining guardianship. There are a few fine GA attorneys here on AVVO that can provide more detail on the particulars of GA law in this area.
This is not legal advice nor intended to create an attorney-client relationship. The information provided here is informational in nature only. This attorney may not be licensed in the jurisdiction which you have a question about so the answer could be only general in nature. Visit Steve Zelinger's website: http://www.stevenzelinger.com/
Steven hit this right on the head. Power of attorney will likely not be an option since it would require both his consent and his cognitive recognition ability to understand the document. There is a mechanism in place to deal with your situation, and it is a Guardianship proceeding. Contact a local attorney and they will get you started.
You would need to have a guardianship attorney file a petition.
Doctor's will examine your son and make a recommendation to the court.
Good luck to you.
The answer given does not imply that an attorney-client relationship has been established and your best course of action is to have legal representation in this matter.