Need clarity on school admissions

I’m currently a junior in India, I’m studying commerce under CBSE curriculum, we’re moving to New Jersey this May after finishing my 11th grade, so what will be the procedure and requirements to study there in a public school ?

In the US, public schools are free of charge. Public schools serve residents of a specific geographic area only. (The term “public school” is different than that used in England.)

Private high schools are also referred to as “college prep schools” or just as “prep schools”. They charge tuition & require an application in order to be considered for admission.

Google your town’s name and “Registering for School” to find out how to register for your town/area’s public school.
Bring syllabi of your previous classes so it will be easier for them to know what classes to place you in.
(Assuming Public = free schooling provided by local government)

If you mean a Private school you pay for, you need to look up nearby private schools and look into their admissions policies (and dates…you may possibly may need to apply now)

As an aside, if you aim to attend college, you may need to start over in 11th grade in order to complete graduation requirements.
There are no “tracks” in US schools and all students are mixed although classes are separate depending on achievements - for commerce, you’d be on track for AP econ, AP Gov, Ap calc AB and Ap stats.
You would need to take US history, US Gov (can be regular, honors, or AP) and I think physical education and health (these dont count toward college requirements but for HS).
Since your parents probably haven’t saved any money for your college since they couldn’t anticipate their move when you were 5 or 6, look into costs at public universities in NJ and ways to get merit scholarships. These often depend on doing well on standardized tests.
Have you ever taken the SAT or Act?
Before CBSE, did you take IGCSEs?