Despite the significant advances in vehicle automation and electrification, the next-decade aspirations for massive deployments of autonomous electric mobility on demand (AEMoD) services are still threatened by two major bottlenecks, namely the computational and charging delays. This paper proposes a solution for these two challenges by suggesting the use of fog computing for AEMoD systems, and developing an optimized charging scheme for its vehicles with and multi-class dispatching scheme for the customers. A queuing model representing the proposed multi-class management scheme with sub-class service is first introduced. The stability conditions of the system in a given city zone are then derived. Decisions on the proportions of each class vehicles to partially/fully charge, or directly serve customers of possible sub-classes are then optimized in order to minimize the maximum response time of the system. Results show the merits of our optimized model compared to a previously proposed scheme and other non-optimized policies.