In this paper, we introduce the concept of derivation $d_{a, \beta}$ of ordered $\Gamma$-semiring. We study some of the properties of derivation $d_{a, \beta}$ of ordered $\Gamma$-semirings. We prove that if a derivation $d_{a, \beta}$ is nonzero on an integral $\Gamma$-semiring $M$ then it is non-zero on any non-zero ideal of $M$ and we characterize $k$-ideal and $m-k$ ideal using derivation $d_{a, \beta}$ of ordered $\Gamma$-semiring.