The three-dimensional (3D) magnet ${\mathrm{KBaFe}}_2$(${\mathrm{PO}}_4{)}_3$ hosts an effective tetratrillium spin lattice of ${\mathrm{Fe}}^{3+}$ ($S=5\text{/}2$) ions, offering a prototypical platform to study frustration-driven phenomena in 3D. Through magnetization, specific heat, ${}^{31}\mathrm{P}$ nuclear magnetic resonance (NMR), and muon spin relaxation ($\mu \mathrm{SR}$) experiments, supported by first-principles calculations, we uncover an unconventional ground state. Despite strong antiferromagnetic interactions with a large Curie-Weiss temperature ${\theta }_{\mathrm{CW}}=-70\left(2\right)\mathrm{K}$, no magnetic long-range order is observed down to 30 mK. Below $T^{*}\simeq 3.5\mathrm{K}$, the NMR linewidth becomes nearly field independent and the spin-spin relaxation rate $1/T_2$ saturates, accompanied by a two-component relaxation in the transverse nuclear magnetization $M_{xy}$. The latter indicates the emergence of short-range dynamical correlations, which was further corroborated by a robust and field-insensitive broad maximum in specific heat. In $\mu \mathrm{SR}$, we detect neither a static internal field nor spin freezing; instead, the spins remain dynamic down to 30 mK and the asymmetry curves are best described by two coexisting dynamic relaxation channels: a dominant fast (sporadic) channel and a slower Markovian component. Their differing weights and fluctuation rates suggest microscopic inhomogeneity in spin dynamics. These persistent low-temperature spin fluctuations are found to be intrinsic to the 3D frustrated tetratrillium geometry, exemplifying ${\mathrm{KBaFe}}_2$(${\mathrm{PO}}_4{)}_3$, a rare 3D antiferromagnet with a classical spin that fosters unconventional dynamics.

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• Frustrated magnetism
• Spin dynamics
• Spin liquid