In August 2017, Baturina joined Dinamo Zagreb together with his younger brothers Martin and Marin.
[2] On 17 July 2020, Baturina was signed by Nemzeti Bajnokság I club Ferencváros.
[4] On 20 July 2023, Baturina moved to Portugal, signing a four-year contract with Primeira Liga club Gil Vicente.
[5] On 15 January 2024, after having scored 3 goals and provided an assist in 19 appearances in all competitions for the Barcelos-based side, he returned to Racing on loan until the end of the season.
[6][7] On 22 July 2024, Baturina was loaned to fellow Spanish second division side Málaga, for one year.