In this work, we introduce the new concepts of fuzzy $(h,\beta )$-contractive mapping via triangular $(h,\beta ) $-admissible mappings. Later, we prove some fixed point results for some mappings that provide fuzzy $(h,\beta )$-contractibility and triangular $(h,\beta ) $-admissibility in complete non-Archimedean fuzzy metric spaces. Some examples are supplied in order to support the useability of our results. Our main results substantially generalize and extend some known results in the existing literature.