Ultra-reliable and low-latency communication (uRLLC) plays an important role in the development of 5G-advanced and 6G wireless networks. Combining unmanned aerial vehicles (UAVs) with non-orthogonal multiple access (NOMA) offers a promising solution to achieve improved reliability and lower latency. This is made possible by enabling line-of-sight (LoS) links and concurrent transmissions through the use of UAVs and NOMA, respectively. However, because of the inherent openness of wireless channel, uRLLC faces the security challenges against being eavesdropped. Physical Layer Security (PLS) has been proposed as an efficient method to secure uRLLC, since it uses only the properties of wireless channels (such as fading, interference, and noise). Although the potential benefits of NOMA-UAV provide a better coverage for ground users, it remains a significant challenge since it may provide a LoS link to eavesdroppers. Therefore, in this paper, we investigate the security and reliability performance of UAV and NOMA based uRLLC scenario, under which UAV serves two different types of users with different needs, i.e., secret users and public users. By using stochastic geometry tools, we derive the closed-form expression of the secrecy rate, an important metric in the study of PLS. Additionally, the secure performance is enhanced by maximizing the secrecy rate through optimizing the hovering height and power assignment of UAV. It should be noted that the hovering position is optimized via power allocation when there is only one secret user. Evaluations demonstrate the effectiveness and correctness of our theoretical analysis.