I was responding to the poster’s question about public schools in New Jersey, specifically Newark in Essex County, NJ.
As far as fee-based private/parochial schools: Yes, those will go through an application and selection process. Based on several kids I know who attended local (Bergen County) parochial schools, a “decent” student has a good likelihood to get in.
As far as public magnet schools (such as County Academies, Vocational Schools,…) those are highly selective and I suspect that one might not be able to “transfer” into them. I believe the Newark public school system has it’s own magnet high school – not sure if Essex county offers one by now.