Here are some studies about vitamin D and schizophrenia:
Vitamin D Supplementation During the First Year of Life and Risk of Schizophrenia: A Finnish Birth Cohort Study (2004)
Conclusion: A North Finland birth cohort study found that male newborns who regularly received vitamin D supplementation had a lower risk of developing schizophrenia later in life.
A Systematic Review and Meta-Analysis of Northern Hemisphere Season of Birth Studies in Schizophrenia (2003)
Conclusion: Schizophrenics tend to be born more in winter and spring compared to other seasons, when vitamin D-creating UVB radiation is less available. They also tend to be born more in latitudes farther away from the equator, which get less UVB radiation.
Conclusion: “Low levels of maternal vitamin D may be associated with an increased risk of schizophrenia.”