He later moved to Košice, where he rose through the youth team ranks, making his first-team debut for the club at the age of 17 as a late substitute during a 1–0 home win against Slovan Bratislava.

[5][6] On 30 July 2015, Duda was hit by a stone in Legia's UEFA Europa League qualifier away at Kukesi in Albania, being stretchered off and the match abandoned.

The game was awarded as a 3–0 Legia victory and their opponents were fined €70,000 and forced to play their next European home match behind closed doors.

Even though Hertha had failed to qualify for any European competitions in the subsequent season, finishing 11th and 11 points behind Europa League positions, Duda was spotted and inquired about by Sevilla, as reported in mid-May 2019.

Appointment of Jürgen Klinsmann,[13] a former World Cup winner and a successful international manager, on 29 November 2019, was traced to be a partial reason for Duda's absence from the first team.

[22] Duda made his international debut for Slovakia on 18 November 2014, replacing Marek Hamšík in the 59th minute of a 2–1 friendly win over Finland in Žilina.

[25] His first goal in any of the qualifying competitions was scored in the 10th game of the 2018 FIFA World Cup qualification against Malta (3–0 win), sealing the second place in the group for Slovakia.

Duda was a regular member of the national team under Pavel Hapal as well as Štefan Tarkovič, although commonly unavailable due to injuries.

In March 2023, following a goal-less home draw versus Luxembourg, Erik Farkaš of Denník Šport wrote critically of Duda's overall national team performances arguing that despite prime age of 28 years, he did not appear capable of replacing Marek Hamšík after his international retirement in creativity and game organisation, though he was often fitted into the position by multiple experts.