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We introduce a novel approach to constructing ternary addressable physically unclonable functions (TAPUFs) using magnetoresistive random-access memory (MRAM) devices. TAPUFs use three states (1, 0, and X) to track unstable cells. The proposed TAPUF leverages the resistance properties of MRAM cells to produce unique digital fingerprints that can be effectively utilized in cryptographic protocols. We exploit the cell-to-cell variations in resistance values to generate reliable cryptographic keys and true random numbers, which can add protection against certain attacks. To evaluate the performance of the TAPUF, various tests were conducted, including assessments of inter-cell to intra-cell variation, inter-distance, bit error rate (BER), and temperature variation. These experiments were conducted using a low-power client device to replicate practical scenarios. The obtained results demonstrate that the proposed TAPUF exhibits exceptional scalability, energy efficiency, and reliability.