So you're taking a partial drop and joining a private clg this year, then next year at the time of JEE counselling you need to submit the Transfer certificate(TC) from your private clg but not your Class 12 school TC.
Because JEE counselling need your most recent TC to confirm that you've officially left that institute.Hence now after joining the private clg get TC from there next year and then use it in JEE Counselling.