UAVs have the qualities of large coverage, flexible deployment, scalability, low cost and easy programming. Myriad UAVs are flexibly deployed in the air, on the ground and even on submarines, enabling ubiquitous connectivity. Thus, UAV-assisted IoT is considered a potential solution to support time-sensitive applications in sixth-generation (6G) networks. Such as the Industrial Internet of Things (IIoT), smart homes, smart cities and self-driving vehicles. A large amount of sensor data will be collected and carried by drones for transmission to destination nodes for further processing and analysis. Unlike traditional broadband services, most IoT applications transmit short and time-varying data packets carrying sensor updates. Many studies on time-sensitive applications at this stage still focus on optimization of latency, reliability and other metrics. Less attention has been paid to the freshness of the updates and the timeliness of the data. Age of Information (AoI) is a new metric introduced for time-sensitive applications in recent years. Unlike latency, which represents real-time, AoI utilizes the concept of freshness to depict the timeliness of data. The larger the AoI, the less fresh and timely the information is. To better serve time-sensitive applications, we cannot reduce the stringent requirements for latency while ensuring data timeliness. Therefore, we propose Freshness-based Admission in First Out (FAIFO), a novel fine-grained programmable packet scheduling scheme. FAIFO can guarantee the freshness of information for time-sensitive applications while meeting their low-latency requirements. FAIFO first uses the concept of admission control to rapidly filter high-priority (low-latency) packets into queue A to meet the real-time requirements of time-sensitive applications. Subsequently, depending on the freshness level of the packets, FAIFO will decide whether the discarded packets need to be cached in queue B to meet the timeliness requirements of time-sensitive applications. Finally, we improve the credit-based shaper (CBS) algorithm to perform traffic shaping on packets in queue A and queue B to ensure that high-priority queue A is forwarded first and freshness queue B is forwarded in a timely manner. Simulation experiments compare FAIFO with the ideal benchmark Push-In-First-Out (PIFO), state-of-the-art SP-PIFO, and AIFO. The results indicate that our FAIFO can also obtain the approximate PIFO effect, and the delay guarantee is comparable to SP-PIFO and AIFO. More importantly, FAIFO’s guarantee of information freshness is significantly better than other compared algorithms.