Provisional results put him ahead of the New Patriotic Party's (NDC) Charles Opoku and the Liberal Party of Ghana's (LPG) Bernice Enyonam Sefenu.
Quayson secured 57.4% of the votes (17,205) while Charles Opoku followed with 11,389 votes (42%).
Sefenu trailed behind with 85 votes (0.28%).
The Electoral Commission (EC) is yet to declare the official results of the by-election.
James Gyakye Quayson
But Quayson took to his Facebook page to thank the people of Assin North Constituency for giving him another chance.
In the 2020 elections, Gyakye Quayson secured 17,498 representing 55.2% whiles Abena Durowaa Mensah of the NPP polled 14,193 representing 44.8%.