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In this paper, we analyze the secrecy and throughput of multiple-input single-output (MISO) energy harvesting (EH) Internet of Things (IoT) systems, in which a multi-antenna base station (BS) transmits signals to IoT devices (IoTDs) with the help of relays. Specifically, the communication process is separated into two phases. In the first phase, the BS applies transmit antenna selection (TAS) to broadcast the signal to the relays and IoTDs by using non-orthogonal multiple access (NOMA). Here, the relays use power-splitting-based relaying (PSR) for EH and information processing. In the second phase, the selected relay employs the amplify-and-forward (AF) technique to forward the received signal to the IoTDs using NOMA. The information transmitted from the BS to the IoTD risks leakage by the relay, which is able to act as an eavesdropper (EAV) (i.e., an untrusted relay). To analyze the secrecy performance, we investigate three schemes: random-BS-best-relay (RBBR), best-BS-random-relay (BBRR), and best-BS-best-relay (BBBR). The physical layer secrecy (PLS) performance is characterized by deriving closed-form expressions of secrecy outage probability (SOP) for the IoTDs. A BS transmit power optimization algorithm is also proposed to achieve the best secrecy performance. Based on this, we then evaluate the system performance of the considered system, i.e., the outage probability and throughput. In addition, the impacts of the EH time, the power-splitting ratio, the numbers of BS antennas, and the numbers of untrusted relays on the SOP and throughput are investigated. The Monte Carlo approach is applied to verify our analytical results. Finally, the numerical examples indicate that the system performance of BBBR is greater than that of RBBR and BBRR.