In this paper, we introduce the generalized Archimedean triangular norm in Menger probabilistic 2-metric spaces and Non-Archimedean probabilistic 2-metric spaces, and present a characterization of the generalized Archimedean triangular norm. Based on this, and utilizing the iterative method, we investigate the existence and uniqueness of the fixed points for self-mappings or common fixed points for a family of self-mappings under various contractive conditions in Non-Archimedean probabilistic 2-metric spaces. Many new results are obtained, which extend and generalize corresponding results in the literature.