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In this study, polycrystalline intermetallic compounds Ce 3-x Pd 20+x Si 6 (x = 0; 0.5; 1) as well as La-based analogues La 3-x Pd 20+x Si 6 (x = 0; 1) are synthesized. At the same time, R 2 Pd 21 Si 6 (R Ce, La) are new rare earth compounds presented here. An analysis of the crystal structure shows that the increase in x leads to partial (x = 0.5) or complete (x = 1) replacement of Ce/La ions by Pd in one of the two Wyckoff positions, namely, in position 4 a. Ab initio DFT calculations demonstrate good agreement between the determined lattice parameters and those found experimentally for both Ce 3-x Pd 20+x Si 6 (x = 0; 0.5; 1) and La 3-x Pd 20+x Si 6 (x = 0; 1). A comparative analysis of resistivity and specific heat of Ce 3-x Pd 20+x Si 6 with x = 0; 0.5; 1 makes it possible to associate the Ce ions in the 8 c position with Kondo behaviour in all three compositions, which manifests itself in an increase in resistivity with cooling, as well as in a broad peak of the magnetic contribution of specific heat. The Kondo temperature T K ≈ 25 K obtained from the analysis of the temperature dependences of the heat capacity turns out to be the same for all Ce compounds. The appearance of cerium ions in the position 4 a in compositions with х = 0 and х = 0.5 leads to an additional contribution to the specific heat, the value of which increases with decreasing temperature, as well as, to the formation of a coherent Kondo-lattice state with a maximum of the resistivity at T coh ≈ 15 K, followed by the subsequent onset of negative magnetoresistance regime below T inv ≈ 7 K. Apparently, this behaviour is associated with the appearance of spin and orbital correlations proceeding the quadrupole and antiferromagnetic transitions occurring at lower temperatures. Magnetization measurements show more localized character of magnetic moments of Ce ions at T = 2 K in Ce 3 Pd 20 Si 6 as compared to the Ce 2 Pd 21 Si 6. The orthogonal projection of the Ce 3-x Pd 20+x Si 6 (x = 0; 1) structural unit cell and coordination polyhedra of the atoms in 4 a (a) and 8 c (b) crystallographic sites, space group Fm -3 m. [Display omitted] • Novel ternary Ce-based and La-based intermetallides. • Primary study of Ce 2 Pd 21 Si 6 crystal structure. • Replacement of Ce with Pd in one crystallographic position. • Magnetic, transport and specific heat study of new intermetallides. • Role of Ce ions in 4a Wyckoff position in Kondo behaviour of Ce 3-x Pd 20+x Si 6. [ABSTRACT FROM AUTHOR]