While this was a meta study it is still significant because it looked at quite a few OTC supplements and found only the B-family of vitamins to have a positive effect.
The effects of vitamin and mineral supplementation on symptoms of schizophrenia: a systematic review and meta-analysis | Psychological Medicine | Cambridge Core
B vitamins found to reduce symptoms of schizophrenia
"...The authors of the study reviewed 18 clinical trials, examining a total of 832 patients receiving antipsychotic treatment for schizophrenia. While vitamin C and zinc seemed effective in some single trials, B vitamins stood out as beneficial across multiple studies. “Currently, only B vitamins have been found to be effective on a meta-analytic level. Studies which use high-dose B vitamins, or combine multiple B vitamins, seem to be most effective,” said Firth. In these trials, patients saw improvements in total symptom scores, a standard measure of overall mental health. Those in the early years of the illness were found to benefit most."
The effects of vitamin and mineral supplementation on symptoms of schizophrenia: a systematic review and meta-analysis | Psychological Medicine | Cambridge Core
B vitamins found to reduce symptoms of schizophrenia
"...The authors of the study reviewed 18 clinical trials, examining a total of 832 patients receiving antipsychotic treatment for schizophrenia. While vitamin C and zinc seemed effective in some single trials, B vitamins stood out as beneficial across multiple studies. “Currently, only B vitamins have been found to be effective on a meta-analytic level. Studies which use high-dose B vitamins, or combine multiple B vitamins, seem to be most effective,” said Firth. In these trials, patients saw improvements in total symptom scores, a standard measure of overall mental health. Those in the early years of the illness were found to benefit most."