Does narcissism and schizophrenia have anything to do with each other?

No: Schizophrenics may happen to be narcissistic in some isolated findings, but if so, this is more of a coincidence than a relationship between the two entities. Schizophrenics are more likely to be paranoid and introverted with a small to negligible amount of close friends.

No: Narcissism is a personality disorder, featuring grandiosity, egomania, devaluation and objectification of others, feelings of specialness and entitlement. Schizophrenia is one of the psychotic disorders, featuring (typically) auditory and visual hallucinations (and less frequently tactile, gustatory, and olfactory hallucinations.