In this manuscript new oscillation criteria are given for solutions of h-order delay difference equation in the form ∆ E n + p n E n − α = 0 . Here, four cases of p are considered; for α∈N , as oscillatory periodic sequences with periods 2 α,(2 α+1) and ( α+1) , and a quickly oscillating sequence such that p n p n + 1 < 0 . It is well known that coefficient functions has a very important role in the behavior of the solutions of an equation. The coefficients sequence p has been considered as positive sequences in all oscillation criteria so far. But It is considered as a oscillatory periodic sequences and quickly oscillatory sequences for the first time in this study. We use a new technique to prove our results. Also some examples are provided to demonstrate the effectiveness of the main results.