In view of the scarce spectrum resources and inconvenient deployment in wireless communications, this work focuses on an unmanned aerial vehicle (UAV) enabled non-orthogonal multiple access (NOMA) system where a UAV deployed as a base station serves two users by NOMA. A joint power allocation and aerial jamming (PAAJ) scheme is proposed to achieve reliable and secure communications for the system in the presence of a malicious eavesdropper. To be specific, dynamic power allocation is adopted to ensure the reliability of the system and another friendly UAV jammer is introduced to improve the security of the system. The closed-form expressions of connection outage probability (COP), secrecy outage probability (SOP), and effective secrecy throughput (EST) are derived to evaluate the performance of the security-required user in the practical condition of probabilistic line-of-sight (LoS) and non-line-of-sight (NLoS) air-to-ground (A2G) channels. Moreover, the asymptotic EST is analyzed to obtain further insights. Numerical results show the validity of theoretical derivations and the superiority of the proposed PAAJ scheme over benchmark schemes. The EST of the UAV-enabled NOMA communication system outperforms the conventional terrestrial NOMA system at the low transmitting power from the UAV base station. There exists an optimal height of the UAV base station to maximize the EST, which provides a useful framework for designing UAV-enabled communication systems with heterogeneous service requirements.