Baryogenesis requires baryon number violation. Certain extensions to the Standard Model have proposed the existence of an exact, but parity-conjugated, copy of the ordinary elementary particles called mirror particles. Several experiments have been conducted to search for $n-n'$ oscillation and have imposed very strong constrains on its parameters. Recent analyses of some of these experiments have identified anomalies that could suggest the detection of $n-n'$ oscillation. Neutrons, owing to their large magnetic moment, precess upon the application of a magnetic field, and similarly, its mirror counterpart is also affected by the mirror magnetic field. Previous attempts to search for $n-n'$ oscillation have involved (i) disappearance experiments, which isolated the magnetic field dependent loss channel in ultracold neutron storage or transport, (ii) reappearance experiments, which have searched for magnetic field dependent regeneration of neutrons across a barrier, that could only be traversed by a state invisible to the fundamental forces of the standard model, like the mirror neutron, and (iii) by studying the variations in the precession frequency of polarized neutrons upon flipping the direction of the applied magnetic field, which is precisely measured by experiments searching for neutron electric dipole moment. In this work we have presented the statistical sensitivity increase for neutron electric dipole moment measurement based search for $n-n'$ oscillation by over an order of magnitude compared to [Symmetry {\bf 14}, 487 (2022)], $\tau_{nn'}^{\text{(stat. sens.)}}/\sqrt{\cos(\beta)} \gtrsim 65~\text{s}~(0.36~\mu\text{T}'<B'<1.01~\mu\text{T}'$, at $95\%$ C.L., where $\beta$ is a fixed angle between the ambient mirror magnetic field and the applied magnetic field, as would be the case if the ambient mirror magnetic field has terrestrial origins. Furthermore, we have for the first time, also presented the statistical sensitivity for modulations of the difference in the precession frequency, upon flipping the direction of the magnetic field, as a means of accessing $n-n'$ oscillations, in the case of a galactic source of ambient mirror magnetic field. This has allowed us to demonstrate a $95\%$ C.L. sensitivity of $\tau_{nn',\Omega_{\oplus}}^{\text{(stat. sens.)}} \gtrsim 43~\text{s}~(0.36~\mu\text{T}'<B'<1.02~\mu\text{T}')$ and $\tau_{nn',2\Omega_{\oplus}}^{\text{(stat. sens.)}} \gtrsim 51~\text{s}~(0.36~\mu\text{T}'<B'<1.03~\mu\text{T}')$, with existing data. These constraints could be further improved with the help of the next generation neutron electric dipole moment experiments.