In this study, we employ the distributed phase screen method to simulate the transmission of Autofocusing Airy beams (AAB) with a new kind of power-exponent-phase vortex (NPEPV) through oceanic conditions, including the effects on light intensity and scintillation. We observe that during the oceanic transmission of an AAB with NPEPV, the beam's main ring progressively divides into fan-shaped sections that match the number of topological charges, with the ring maintaining its integrity without splitting at higher power indices. Furthermore, the scintillation index for AAB with NPEPV decreases as the topological charge increases, up to 400 m. Beyond this distance, the beam structure is significantly disturbed and the relationship between scintillation index and topological charge becomes irregular. Additionally, a higher power index results in a smaller scintillation index slope over the transmission distance and smoother fluctuations in the scintillation factor. At the same transmission distance, a smaller girdle radius leads to a lower scintillation index for AABs with NPEPV.