Let R be a commutative ring with a nonzero unity element. In this article, we introduce and examine new classes of ideals in Z2-graded rings, expanding upon the earlier concept of N-prime ideals. Using the function N : R → R0, defined by N(x) = x0 2 – x1 2 for x = x0 + x1 ∈ R, we define and analyze two new types of ideals, 2-N-prime and weakly 2-N-prime ideals. A proper ideal I is called 2-N-prime if xy ∈ I implies that N(x2) ∈ I or N(y2) ∈ I. Similarly, I is weakly 2-N-prime if 0 ≠ xy ∈ I implies that N(x2) ∈ I or N(y2) ∈ I. We explore the fundamental properties of these ideals, highlighting their connections to established structures in graded ring theory. Through examples and counter examples, we illustrate the differences between 2-N-prime and weakly 2-N-prime ideals, underscoring their significance in the theory of graded rings. These results not only deepensour understanding of ideal theory in Z2-graded rings but also open new avenues for futures research.