Do people with autism or Asperger's syndrome have a higher genetic predisposition to psychosis or schizophrenia than that of healthy people?
Generally speaking, yes; it's relatively more common for psychosis to be comorbid with or present after diagnosed Autism.
For a good overview of this topic read Autism and Schizophrenia (Yael Dvir, MD and Jean A. Frazier, MD).
COS (Child Onset Schizophrenia)—the onset of psychosis before age 13 years—is considered a rare and severe form of schizophrenia. Systematic studies of COS show high rates of the disorder being either preceded by or comorbid with autistic spectrum disorders (ASD).7
Note however that the similar (but not identical) features between COS and Autism:
Although the disorders are distinct, they have shared clinical features. Social withdrawal, communication impairment, and poor eye contact seen in ASD are similar to the negative symptoms seen in youths with schizophrenia.11 When higher-functioning individuals with autism are stressed, they become highly anxious and at times may appear thought-disordered and paranoid, particularly when they are asked to shift set (such as being asked to change a topic of conversation or to stop an activity that they are engaged in and begin a new activity).12 A subset of children (28%) in the ongoing NIMH study of COS have been reported to have comorbid COS and ASD.7
There's also likely a bit of sample bias going on; children presenting severe symptoms of either Autism or COS are logically much more likely to be seen by medical professionals than neurotypical children or those who may have Autism but present less significant external symptoms. So take the specific percentages with a grain of salt, but the two certainly seem to be related.