Recent progress in electric vertical take-off and landing (eVTOL) vehicles suggests that soon these vehicles could safely and efficiently transport people and cargo in urban areas. Therefore, advanced air mobility vehicles could become an alternative means of transport to overcome traffic congestion in cities in the upcoming years. There has been enormous interest from companies and governments in recent years in developing such technologies and enabling markets for new air transportation services. Despite the interest in the topic, little research has been done to address the aircraft scheduling problem in advanced air mobility take-off and landing areas (vertiports). The vertiports serve as the airports of eVTOL vehicles and could experience congestion problems similar to those of airports. This work proposes two optimization models for scheduling departing and landing aircraft at the vertiports’ common ground taxi routes (taxiways), gates, and touchdown and lift-off (TLOF) pads. The mathematical models include advanced air mobility features such as separation rules and blocking constraints. As scheduling objectives, the first model maximizes the vertiport throughput, and the second model minimizes the deviation from the expected take-off/landing time. In addition, as a solution methodology, we developed two heuristic algorithms that use scheduling rules to assign and sequence the aircraft to the vertiport components. Computational results show that the optimization models find optimal schedules for small-sized instances of up to 10 aircraft, while the heuristic algorithms provide good results in terms of solution quality and computational time for large instances.