I got 96.08 percentile in JEE Mains. What would be my Rank and what colleages would i get in south India based on this percentile.

Hello, based on your Paper-1 percentile your Overall Rank is expected to be in between 40102 - 45080. You have not mentioned which category you belongs to and what is your home state. So, assuming you belong to General Category you have chances of getting some good colleges.
Through JEE Mains you can get seat in top private Engineering Colleges in South India.

For your percentile you have chances of getting below NITs based on previous year's ranks.
1. National Institute of Technology, Meghalaya
2. National Institute of Technology, Nagaland
3. National Institute of Technology, Raipur
4. National Institute of Technology, Sikkim
5. National Institute of Technology, Arunachal Pradesh
6. National Institute of Technology, Puducherry
7. National Institute of Technology, Patna
8. National Institute of Technology, Hamirpur
9. National Institute of Technology, Goa

You can use below link to predict more colleges in which you have chances of getting seat.

https://engineering.careers360.com/jee-main-college-predictor?icn=QnA&ici=qna_answer

Useful Links for you-
Rank Predictor-
https://engineering.careers360.com/jee-main-rank-predictor

Cutoff-
https://engineering.careers360.com/articles/jee-main-cutoff

Official cutoffs for NITs, IIITs, IITs, CFTIs-
https://josaa.nic.in/Result/Result/currentorcr.aspx

All The Best!!