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The surface states of 3D topological insulators in general have negligible quantum oscillations (QOs) when the chemical potential is tuned to the Dirac points. In contrast, we find that topological Kondo insulators (TKIs) can support surface states with an arbitrarily large Fermi surface (FS) when the chemical potential is pinned to the Dirac point. We illustrate that these FSs give rise to finite-frequency QOs, which can become comparable to the extremal area of the unhybridized bulk bands. We show that this occurs when the crystal symmetry is lowered from cubic to tetragonal in a minimal two-orbital model. We label such surface modes as ‘shadow surface states’. Moreover, we show that the sufficient next-nearest neighbor out-of-plane hybridization leading to shadow surface states can be self-consistently stabilized for tetragonal TKIs. Consequently, shadow surface states provide an important example of high-frequency QOs beyond the context of cubic TKIs.