Kóša joined Spartak Trnava on 18 July 2020.[2] He scored his first league goal against AS Trenčín the same year on 25 October, breaking Josef Adamec's record as Spartak Trnava's youngest goalscorer at the age of 17 years, 1 month, and 11 days.[3] In February 2022, Kóša was named the Best Player of Slovakia in the U19 category at Grassroots Football Gala hosted by the Slovak Football Association.[4]
At the age of 17 in 2021, Kóša became the youngest player of the Slovakia U21 national team, playing the full match against Lithuania and Northern Ireland.[6]