This work presents a systematic characterization of the quasi-periodic dynamics of a uniaxial anisotropic magnetic nanoparticle under the influence of a time-varying external magnetic field. Using the Landau–Lifshitz–Gilbert (LLG) formalism, we analyze the response of the system as a function of key parameters, particularly focusing on the effects of magnetic anisotropy and dissipation. Through an extensive numerical exploration, we identify transitions between periodic, quasi-periodic, and chaotic regimes, employing Lyapunov exponents, isospike diagrams, Fourier spectra, and winding number calculations. The results reveal that the anisotropy parameter strongly influences the asymmetry of the dynamical states, leading to distinct behaviors along the easy and hard anisotropy axes. Additionally, at low dissipation, direct transitions between quasi-periodic and chaotic states emerge as a function of the external field, while at higher dissipation, periodic states dominate. The winding number analysis uncovers complex hierarchical structures, including self-similar step-like formations characteristic of the so-called Devil's staircase phenomenon, along with a granular transition mechanism between quasi-periodic and chaotic states. Furthermore, the role of initial conditions is explored, demonstrating the presence of multistability, where different attractors coexist depending on the initial configuration. These results contribute to a deeper understanding of the nonlinear magnetization dynamics in anisotropic nanoparticles and may serve as a reference for future studies exploring the influence of quasi-periodic behavior in spintronic systems.