For two integers \(1\le j\le k\) , we define (k, j)-colored partitions to be those partitions in which parts may appear in k different types and at most j types can appear for a given part size. Let \(c_{k,j}(n)\) be the number of (k, j)-colored partitions of n. Recently, Keith studied (k, j)-colored partitions and proved the following results: For \(j\in \{2,5,8,9\}\) , we have \(c_{9,j}(3n+2)\equiv 0\pmod {27}\) for all \(n\ge 0\) . For \(j\in \{3,6\}\) , we have \(c_{9,j}(9n+2)\equiv 0\pmod {27}\) for all \(n\ge 0\) . In this paper, we determine all a, b, c, j with \((a,b)=1\) and \(1\le j\le 8\) such that \(c_{9,j}(an+b)\equiv c\pmod {27}\) for all nonnegative integers n.
