On $\mathrm{\ell }-$regular and $2-$color partition triples modulo powers of $3$

Let $T_{\mathrm{\ell }}(n)$ denote the number of $\mathrm{\ell }-$regular partition triples of $n$ and let $p_{\mathrm{\ell },3}(n)$ enumerates the number of 2–color partition triples of $n$ where one of the colors appear only in parts that are multiples of $\mathrm{\ell }$. In this paper, we prove several infinite families of congruences modulo powers of 3 for $T_{\mathrm{\ell }}(n)$ and $p_{\mathrm{\ell },3}(n)$, where $\mathrm{\ell }\ge 1$ and $\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}{3}^k)$, and $\equiv \pm 3^k(\mathrm{m}\mathrm{o}\mathrm{d}{3}^{k+1})$.