Physical Unclonable Functions (PUFs) offer the natural advantage of built-in key generation, thus eliminating the costly process of embedding unique key after manufacturing millions of integrated circuits. When PUFs are deployed for the application, all the Challenge-Response Pairs (CRP) are collected and stored in a trusted server, and the responses are compared with the one from the device during the run-time - forming the crux of various security protocols. Two issues are commonly faced during PUF designs. First, to enhance the applicability of PUF, larger set of CRP is desirable, which is referred to as a strong PUF. Second, due to the emergence of machine learning-based PUF modelling attacks, it is now imperative to have a PUF demonstrating resistance against such attacks. In this paper, we propose a novel Parity Resistive RAM PUF (PR-PUF) implemented using RRAM crossbar architecture. PR-PUF supports low-overhead reconfiguration, where both the original and reconfigured CRP space enhances the CRP size, with average uniqueness between reconfiguration of 49.98%. The construction also demonstrates excellent robustness against various modelling attacks. We present detailed design analysis and circuit-level simulation studies.