Early career Štefan started his career at FK Hanušovce nad Topľou, Bukóza Vranov nad Topľou and was later transferred to 1. Football Club Košice where he spent three seasons. He was signed by MFK Ružomberok in the summer of 2002 at the age of 18.
Zošák was captain of MFK Ružomberok.
In June 2010, he joined Slovak club MŠK Žilina. He played 22 matches in his first season.
He qualified with Žilina to the 2010-2011 Union of European Football Associations Champions League and played 2 group games. In the next season he made 4 appearances for Žilina.
On January 2012 Zošák joined to Slovak club 1.
Football Club Tatran Prešov, on a half-year loan from MŠK Žilina. He made his debut for 1. Football Club Tatran Prešov against MFK Košice on 3 March 2012.
He then continued his career in Football Club Nitra before returning to Ružomberok in summer 2013.
Zošák participated at the 2003 Fédération internationale de football association World Youth Championship for Slovakia and played a match against Brazil in the round of 16. Ružomberok International.