In this work, we propose a Fog-enabled UAV-as-a-Service (FU-Serve) architecture to address the issues of data transmission delay for serving time-critical Internet of Things (IoT) applications. Traditionally, in a UAV-as-a-Service (UaaS) platform, different UAVs host heterogeneous sensors, which sense the physical phenomenon and transmit the sensed data to a centralized entity. Transmission of data from the sensors to the centralized entity and making any decision for an application consumes a significant amount of time. Consequently, the traditional UaaS architecture is unsuitable for serving time-critical IoT applications such as transportation, healthcare, and industries. To address these issues of service latency for time-critical IoT applications, we present the FU-Serve architecture by introducing the concept of fog computing in the UaaS platform. We discuss all the components of FU-Serve elaborately in this paper. Additionally, we architect optimal and dynamic fog node selection mechanisms for FU-Serve, which reduce the transmission delay in the networks. The simulation results show that the FU-Serve outperforms by 75% compared to the traditional UaaS platform.