According to Rytov approximation theory, we derive the analytical expression of the detection probability of the autofocusing Airy beam (AAB) with powerexponent-phase carrying orbital angular momentum (OAM) mode, AAB-PEPV. We analyze the influence of oceanic turbulence on the propagation characteristics of the AAB-PEPV. The results show that the AAB-PEPV beam has a higher detection probability at the receiver when the anisotropic ocean turbulence has a larger unit mass fluid dynamic energy dissipation rate, a larger internal ratio factor, and a higher anisotropy factor. At the same time, the detection probability decreases with the temperature change dissipation rate, the temperature and salinity contribution to the refractive index spectrum. In addition, the larger power exponential phase and the longer wavelength the AAB-PEPV beam has, the better anti-interference the AAB-PEPV beam has.