In this paper, we study the distribution of zeros and the uniqueness of certain type of differential-difference polynomial of the form \((f^n(z)P[f](z)H(z,f))^{(k)}\) sharing a small function with the notion of weakly weight and relaxed weight, where f be transcendental meromorphic function of finite order, P[f] is a differential polynomial of f defined as (1) and H(z, f) is a difference polynomial of f defined as (2). We introduce a constructor U(z, w) to show the number of omitted values of P[f]. As some applications, we extend many previous results of entire functions due to Banerjee and Majumder (Anal Math, 43:415–444, 2017) and Majumder and Saha (Ukrainian Math J, 73:791–810, 2021) to the case of meromorphic functions.
