We investigate the finite-size effects, energy spectra, and thermodynamics of a spin-$\frac{1}{2}$ trimer, a three-sided star tetramer, and tetrahedron clusters with Heisenberg and bond-dependent Kitaev exchange. Using exact diagonalization, we compare the isotropic-exchange case with the corresponding Heisenberg-Kitaev clusters in an applied magnetic field. The Kitaev term lifts degeneracies, hybridizes states with different total-spin character, and produces nonlinear field-dependent eigenvalues associated with avoided crossings. These spectral changes generate field-driven cluster transitions, including first- and second-order ground-state transitions associated with level crossings and continuous ground-state evolution. They also redistribute finite-level Schottky weight in the magnetic heat capacity and can produce additional low-temperature heat-capacity features when the ratio $K/J$ is large. The results provide analytic cluster benchmarks for identifying how bond-dependent symmetric anisotropic exchange modifies spectra, entropy, and heat-capacity response in molecular-magnet and cluster-based spin systems. It should be noted that while these calculations provide insight into the individual Kitaev interaction, finite-size effects mean this does not fully carry over to bulk systems that exhibit quantum spin liquid behavior.

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• Electronic & magnetic properties of clusters
• Specific heat
• Antiferromagnets
• Exact diagonalization
• Heisenberg model
• Kitaev-Heisenberg model