Congress is leading on three constituencies out of four in Punjab while Shiromani Akali Dal (SAD) is ahead on one seat.
The counting of votes is underway for the assembly seats of Dakha, Jalalabad, Mukerian and Phagwara that went to bypolls on October 21.
In Punjab, Congress formed the government in 2017 after winning a majority in Assembly elections.
The Phagwara seat fell vacant after its legislator Som Parkash was elected to the Lok Sabha earlier this year from Hoshiarpur.
Dhaka constituency is one of the most keenly watched contests- a direct conflict between Congress and Akalis. Sandeep Sandhu, political secretary of Chief Minister Amarinder Singh, is the Congress candidate, who is pitted against SAD's Manpreet Singh Ayali.
The seat got vacant after former AAP leader and noted Supreme Court lawyer H S Phoolka resigned from the state assembly in October last year over the Congress government's alleged failure to take action against those involved in the desecration of religious sects in 2015 in Punjab.
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Jalalabad, another Akali bastion, fell vacant after SAD chief Sukhbir Singh Badal got elected to the Lok Sabha from Ferozepur parliamentary constituency.
In the recently held by-elections for Jalalabad, there is a straight contest between SAD's Raj Singh Dibipura and Congress's Raminder Singh Awla.
In the 117-member Punjab Assembly, the Congress at present has 77 seats, SAD 13, AAP 19, BJP 2, Lok Insaaf Party 2.