Dyck paths on colored lattices

Fried recently enumerated Dyck paths having equally many black and white cells below them, for the chessboard coloring (Narayana numbers) and the column-alternating coloring (Fuss–Catalan numbers). We prove a generalization here: for the coloring of columns modulo any $c\ge 2$, the number of Dyck paths of semilength $n$ whose $c$ residue classes carry equal weight is the Raney number ${\text{Raney}}_{c+1,r}(m)$, where $n=cm+r-1$.