Energy harvesting-aided non-orthogonal multiple access (NOMA) meets critical requirements of modern wireless networks in terms of spectral efficiency, communication reliability, and energy efficiency. However, information security for it has not received greatly attentions from both industry and academia. This paper proposes jammer selection to meliorate its security performance. To promptly assess the efficacy of the proposed jammer selection, we propose explicit formulas of connection/secrecy throughput and outage probability for both far and near users accounting for non-linear feature of energy harvesters. These formulas are corroborated by Monte-Carlo simulations and quickly generate innumerable results to reveal a significant/slight influence of energy harvesting nonlinearity on communications reliability/information security. In addition, there exist limits on target data/secrecy rates to avoid complete connection outage (i.e. connection outage probability is one) and achieve complete security (i.e. secrecy outage probability is one). Additionally, the proposed (NOMA-and-proposed jammer selection) scheme significantly outperforms its counterparts (NOMA-and-random jammer selection and orthogonal multiple access-and-proposed jammer selection) in terms of both security and reliability. Nevertheless, there is a trade-off between reliability and security. Notably, the proposed scheme obtains optimum security/reliability performance with proper selection of time/power splitting coefficient.