His grandfather, Leon, was a veteran of the January uprising and mayor of Filipów and Sereje, both near Suwałki, Koc's hometown, while his grandmother, Waleria, was part of the Polish National Government. Adam's father, Włodzimierz (1848-1925) was a teacher of ancient languages. His marriage with Helena ("née" Pisanko) brought three children: Stefan (1889-1908), Adam Ignacy himself and Leon Wacław, the youngest of them (1892-1954).