That's a really good idea to have your dog accepted as a service dog.

He climbs into your lap to comfort you when you are depressed.
He encourages you to have routine in your day, and helps you feel safe when you're out walking.
He helps you to focus on outside stimuli when you're being overwhelmed by paranoia or psychosis.

I think those three things should qualify him as a service dog, and you may be allowed to bring him in patient with you.