In this paper, we study the value distribution and uniqueness of linear 
-difference polynomial 
and its -difference operator 
, for a transcendental meromorphic function 
having zero order. Our results extends, improves and generalizes some of the earlier results due to Thin [Thin, N. V. Uniqueness of meromorphic functions and 
-difference polynomials sharing small functions. Bull. Iranian Math. Soc. 43 (2017), no.~3, 629–647]; Dyavanal and Desai [Dyavanal, R. S.; Desai, R. V. Uniqueness of -shift difference polynomials of meromorphic functions sharing a small function. Math. Bohem. 145 (2020), no.~3, 241–253].
