Regional air mobility refers to the transportation of passengers aboard small aircraft over short distances. These operations are challenging due to low passenger volumes, competing transportation modes, and high operating costs. Nevertheless, the recent convergence of new technologies for electric propulsion and autonomy brings the promise of step-changes in both operating efficiency and sustainability. The next challenge is to define concepts of operations that best use these advanced aircraft. We develop a modeling and optimization environment to address this challenge by first estimating the passenger demand for regional air mobility, and then by concurrently optimizing the fleet assignment and scheduling of these operations. This helps identify the optimum fleet composition and the network of routes that best serve this demand. The contribution of this research is the formulation of the optimization as a half-leg half-itinerary mixed-integer linear program using a hierarchical multi-objective approach that provides insights about trade-offs between profitability and emissions. We demonstrate the ability of this environment to solve large fleet assignment and scheduling problems to near optimality by applying it to the United States Northeast Corridor using a fleet of electric and hybrid-electric regional aircraft. Results highlight that the transition to an electrified fleet allows serving twice the number of communities currently served, while reducing the carbon emissions per passenger by fifty percent. With improving battery specific energy density, many more untapped markets can be served profitably and sustainably, and many smaller communities can get connected to the rest of the National Airspace System.