The ThCrSi structure type has been well explored for decades with diverse magnetic, superconducting, and heavy-fermion behavior. For transition metal-containing ThCrSi-type compounds, a metallic band structure and properties are typical. In this work, a rare example of semiconducting BaCuTP (T = Al, Ga, In) materials is reported. BaCuTP materials retain the tetragonal I4/mmm ThCrSi-type crystal structure with a large c/a ratio of ∼3.3, where Cu and T metals jointly occupy the Cr-site. Edge-sharing (Cu/T)P tetrahedra form [CuTP] layers stacked along the crystallographic [001] direction, with the Ba cations located in the interlayer spaces. Solid state NMR revealed partial short-range ordering in the Cu/T sublattice. The composition of the produced phases is electron balanced, BaCuT(P). High values of Seebeck coefficients were experimentally observed due to the high valley degeneracy in the band structure. Heat capacity and structural studies show that Ba exhibits anisotropic 'rattling-like' behavior along the [001] direction in Ga- and In-containing compounds. A combination of Ba rattling, short range Cu/T ordering, and a recently discovered coupling between acoustic and optical phonons for ThCrSi-type phosphides, resulted in ultralow thermal conductivity (<0.50 W m K) for the title compounds. © 2024 The Royal Society of Chemistry.