This is not medical advice, just listing some supplements i have experience using with good results 

(NAC) N-Acetylcysteine:
     For the production of glutithione which is found to be commonly low in schizophrenics. Its the bodies most powerful antioxidant.

Aspirin: for lowering inflammation which is a popular linked pathology of the disease

Creatine: for mitochondrial energy production (brain energy)

Probiotics and digestive enzymes for gut health. Schizophrenia has been linked to immune system malfunctions and your gut is the center for immune health