The AAP was racing ahead of its rivals in Punjab leading in 64 seats, according to early trends.
Counting of votes for 117 assembly seats in Punjab began on Thursday amid tight security arrangements.
Ferozepur Rural, Kharar, Lehra, Dharamkot and Attari were among the seats where the AAP was leading.
The SAD was leading in Bholath and Tarn Taran, among others.
In the 117-member Punjab Assembly, the majority mark is 59.
Exit polls on Monday predicted a clear victory for the Aam Aadmi Party (AAP) in Punjab with the scale of the party's victory varying across various surveys