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Let $\overline{p}_{j,k}(n)$ denotes the number of $(j,k)$-regularoverpartitions of a positive integer $n$ such that none of the parts iscongruent to $j$ modulo $k$. Naika et. al. (2021) proved infinite families ofcongruences modulo powers of 2 for $\overline{p}_{3,6}(n)$,$\overline{p}_{5,10}(n)$ and $\overline{p}_{9,18}(n)$. In this paper, we obtaininfinite families of congruences modulo power of 2 for $\overline{p}_{4,8}(n)$,$\overline{p}_{6,12}(n)$ and $\overline{p}_{8,16}(n)$. For example, we provethat, for all integers $n\geq 0$ and $\alpha\geq 0$, $$\overline{p}_{4,8}\left( 5^{2\alpha+1}\left( 16(5n+j)+14\right) \right)q^n\equiv 0\pmod{64}; \qquad j=1,2,3,4.$$

Some New Congruences Modulo Powers of 2 For $(j,k)$-Regular Overpartition