Are there any genetic diseases that produce positive symptoms of schizophrenia?

Not really. Schizophrenia is complicated and I am unaware of a y ''disease'' that is causative.
Yes amd no. There are some rare disorders such as porphyria that can cause symptoms of psychosis. But, that technically is an "organic psychosis, " not schizophrenia. Others are listed on this website: http://www.Medicalnewstoday.Com/releases/160428.Php that said, genes and gene mutations that may contribute to the risk of schizophrenia that are under active investigation.