The special rounds are conducted after the completion of the first seven rounds of the counselling. The process of the first seven rounds of counselling usually gets completed till the last week of July. After which this the special rounds of counselling takes place. During these special rounds of counselling the seats which remain unfilled during the first seven rounds are filled. The detailed schedule will soon be uploaded on the official website of josaa. Hope this helps. 

Hello Rohti, 

I think you are talking about the counseling after the JEE - Main and Advanced and by special rounds you mean the spot rounds after the levels 1 to 6. These rounds are conducted if the seats in any college are unfilled and stay vacant so to fill the vacant seats special rounds are conducted. There are no specific dates for the commencement of these rounds but these occur after all the normal rounds which usually happen in the second half of July or sometimes the first week of August.

All The Best