Though the Asia Cup is considered a small sideshow in the cricket calendar, it has been held sporadically since 1984. India won that first tournament in 1984 and now has a total of 6 titles, including 2016 which was held in the 20-over format for the first time. It is expected that it will be held in this format whenever it is held in the same year as the World T20 Championship.
For the full history see: https://en.wikipedia.org/wiki/Asia_Cup
The leading individual performances are given below:
Most Runs (80 and above)

Somewhat ironically the most runs were scored by a batsman from Hong Kong which played only in 3 matches in the first round. From the “main” teams Sabbir Rahman scored the most runs (176) and was named the “Man of the Tournament”. Babar Hayat and LD Chandimal were the only ones to cross 50 twice.
Highest Individual Scores (50 and above)

RG Sharma made the highest score (83) among the main teams, followed by Sabbir Rahman with 80.
Bowling: 4 or more wickets overall

Among players from the main teams, the lesser-known Al-Amin Hossain took the most wickets (11) followed by Kulasekara, Mohammed Amir and Pandya with 7 apiece.
Best innings bowling: 3 or more wickets

Malinga’s 4-26 is the best performance for the main teams. Unfortuately for Sri Lanka that was the only match he played. The next best is 3-8 by Pandya. Al-Amin Hossain was consistent with three 3-wicket hauls.
Most dismissals (3 and above)

Not surprisingly, Dhoni topped this list along with SP Patil of the UAE. Nurul Hasan had the most stumpings (3). The most catches by non-keepers were 6 by Babar Hayat and Soumya Sarkar.
Overall all-round performance (at least 40 runs and 4 wickets):

Useful contributions by Mahmudullah and Shakib, besides the trio from the UAE.
All-round match performances (at least 20 runs and 2 wickets)

Rohan Mustafa had the best all-round match performance,while Mahmudullah had the best performance among the main teams.
It is interesting to see that India won the tournament without any spectacular performances (except RG Sharma’s 83). The whole performed better than the sum of the parts, which is supposed to be the hallmark of a good team.