Like can a 3 year old show symptoms?

Yes, in very rare cases a 3 or 4 year old can show symptoms. Only about 2 months ago the national media picked up a story of a girl who was very young around 4 and she has symptoms that are very resistant to treatment and they were talking about her taking adult sized doses of antipsychotic drugs that would bring an adult to their knees and it didn't even phase her when she probably weighted less than 50 pounds.. at the time of the story she was being treated inpatient.

Absolutely not. Schizophrenia usually manifests in late adolescence and early adulthood. VERY RARELY older children can be diagnosed with early onset dementia (which is a precursor to schizophrenia), but this diagnoses is very, very uncommon, and would never be given to someone as young as 3.