Despite their ubiquity, the origin of cosmic magnetic fields remains unknown. Various mechanisms have been proposed for their existence including primordial fields generated by inflation, or amplification and injection by compact astrophysical objects. Separating the potential impact of each magnetogenesis scenario on the magnitude and orientation of the magnetic field and their impact on gas dynamics may give insight into the physics that magnetised our Universe. In this work, we demonstrate that because the induction equation and solenoidal constraint are linear with $B$, the contribution from different sources of magnetic field can be separated in cosmological magnetohydrodynamics simulations and their evolution and influence on the gas dynamics can be tracked. Exploiting this property, we develop a magnetic field tracer algorithm for cosmological simulations that can track the origin and evolution of different components of the magnetic field. We present a suite of cosmological magnetohydrodynamical RAMSES simulations that employ this algorithm where the primordial field strength is varied to determine the contributions of the primordial and supernovae-injected magnetic fields to the total magnetic energy as a function of time and spatial location. We find that, for our specific model, the supernova-injected fields rarely penetrate far from haloes, despite often dominating the total magnetic energy in the simulations. The magnetic energy density from the supernova-injected field scales with density with a power-law slope steeper than 4/3 and often dominates the total magnetic energy inside of haloes. However, the star formation rates in our simulations are not affected by the presence of magnetic fields, for the ranges of primordial field strengths examined. These simulations represent a first demonstration of the magnetic field tracer algorithm (abridged).
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