Hello dear candidate,

You didn't mention your Stream or interest in the course you want to pursue further. But in my opinion for the question you've asked.

The answer is "YES" definitely you can get admission to the best college in Tamil Nadu in whatever course you want to pursue, just fill application of various competitive exams and do your best, secure the best possible rank then definitely you will get admission.

Don't lose hope.

Knowledge matters more than Marks.

All the best!

You can go for entrance exams if you think you can do well there.
Getting a good college (Merit -wise) with 60% is quite difficult these days.
My suggestion would be that apply for an entrance exam at any central university.

All the best!