Quasi-periodic oscillations (QPOs), in particular, the ones with high
frequencies, often observed in the power spectrum of black holes, are useful in
understanding the nature of strong gravity since they are associated with the
motion of matter in the vicinity of the black hole horizon. Interestingly,
these high frequency QPOs (HFQPOs) are observed in commensurable pairs, the
most common ratio being 3:2. Several theoretical models are proposed in the
literature which explain the HFQPOs in terms of the orbital and epicyclic
frequencies of matter rotating around the central object. Since these
frequencies are sensitive to the background spacetime, the observed HFQPOs can
potentially extract useful information regarding the nature of the same. In
this work, we investigate the role of regular black holes with a Minkowski
core, which arise in gravity coupled to non-linear electrodynamics, in
explaining the HFQPOs. Regular black holes are particularly interesting as they
provide a possible resolution to the singularity problem in general relativity.
We compare the model dependent QPO frequencies with the available observations
of the quasi-periodic oscillations from black hole sources and perform a \c{hi}
2 analysis. Our study reveals that most QPO models favor small but non-trivial
values of the non-linear electrodynamics charge parameter. In particular, black
holes with large values of non-linear electrodynamics charge parameter are
generically disfavored by present observations related to QPOs.
