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We numerically test quasi-periodic oscillations using three theoretically-motivated models of spacetime adopting neutron star sources. Then, we compare our findings with a spherically-symmetric spacetime inferred from $F(R)$ gravity, with constant curvature, showing that it fully-degenerates with our previous metrics, that have been adopted in the context of general relativity. To do so, we work out eight neutron stars in low mass X-ray binary systems and consider a Reisser-Nordström solution plus a de Sitter phase with unspecified sign for the cosmological constant term. In particular, we investigate three hierarchies, \textit{i.e.}, the first dealing with a genuine Schwarzschild spacetime, the second with de Sitter phase whose sign is not fixed \emph{a priori} and, finally, a Reisser-Nordström spacetime with an additional cosmological constant contribution. We perform Markov chain Monte Carlo analyses, based on the Metropolis-Hastings algorithm, and infer 1--$σ$ and 2--$σ$ error bars. For all the sources, we find suitable agreement with spherical solutions with non-zero cosmological constant terms, \textit{i.e.}, with either de Sitter or anti-de Sitter solutions. From our findings, we notice that the existence of topological contribution to the net charge, suggested from $F(R)$ extensions of gravity, seems to be disfavored. Finally, we focus on the physics of the cosmological constant term here involved, investigating physical consequences and proposing possible extensions to improve our overall treatments.