Is there any special test for schizophrenia done by a clinical psychologist?

Not exactly (read:) Schizophrenia cannot be directly and definitively diagnosed with one physical test, nor on the basis of just one psychological test. If the psychologist can get interview/observation, family interview, record review & (if possible) one or more tests, that is likely sufficient. There are specific tests/interviews, but they are not completely specific to schizophrenia without other data to assist.