Dear aspirant, being in normal private school sometimes makes you feel that it can affect your JEE score. Mine was the same case. But trust me school hardly matters if you are willing and ready to choose the hardworker's path. Many good private schools provide their students extra classes for JEE but it's just to increase their reputation. Students can prepare well at home as all the study material is available online and same is taught by them in schools.
My school teachers taught us just the CBSE syllabus and there were many students in my class who were preparing for JEE. At that time we made our own group started preparing together. If any doubt arises, there was always someone in our group who can come up with the solution.
You can try the same. But remember one thing even after doing this you have to work hard on your own. Choose the right study material and plan everything accordingly.
All the best
Hope this helps

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