Keith (Integers 23, A9, 2023) introduced the simultaneously s-regular, t-regular and s-distinct partition function which counts the total number of partitions of a positive integer n such that none of the parts are divisible by s and t and each part appears fewer than s times. The simultaneously s-regular, t-regular and s-distinct partition function is denoted by \(B_{s,t}^D(n)\) , where \(1<s<t\) are integers. In this paper, we prove some infinite families of congruences for the partition function \(B_{s,t}^D(n)\) for \((s,t)=(3,4)\) , (4, 9), (5x, 5y) and (7x, 7y), where x and y are two positive integers. We also offer congruences of \(B_{s,t}^D(n)\) for prime values of s.
