Hi Asai,

First of all, there is nothing as Government aided in Tamil nadu Medical counselling. Tamil Nadu Medical counselling proceeds as follows.

There are different type of seats for Medicine in Tamil Nadu. 

1. Government Medical Colleges (23 colleges - 3250 seats)

2. Government quota seats of the Self-financing Colleges - (14 colleges - tentative no of seats)

3. Management Quota seats of the Self-financing colleges - (14 colleges - tentative no of seats)

DME has started issuing applications for the government and NRI/Management seats seperately, last date of which is June 20th 5 P.M. 

Now, from your question I assume that you are interested only in the first two options. 

Considering the competition, it is very difficult to get a government seat this year for 340 marks. But you can try for government or qovt. quota seats of Self-financing colleges in BDS. 

All The Best.