Compositional tailoring externally enables the fine tuning of thermal transport parameters of materials using the dual modulation of electronic or thermal transport properties. Theoretically, we examined the lattice dynamics of three particularly ternary representatives with different stoichiometry, BaMgSi, Ba2Mg3Si4, and BaMg2Si2, and identified the inherent bonding hierarchy and rattling Ba atoms, which were responsible for reducing the lattice thermal conductivity. BaMgSi and Ba(2)Mg(3)Si(4)exhibited inherently ultra-low lattice thermal conductivity of 1.27-0.37 W m(-1)K(-1)in the range of 300-1000 K due to the bonding hierarchy and rattling Ba atoms. The low-energy optical phonons are overlapping with the acoustic phonons. This is associated with the intrinsic rattler-like vibration of Ba cations and leads to the characteristic in the localization of the propagative phonons and large anharmonicity. Although BaMg(2)Si(2)had a dumbbell-shaped Si-Si covalent and Ba-Si/Mg ionic bonding environment and intrinsic rattler-like vibration of Ba cations, the middle frequency optic phonon branches contribute considerably to the thermal conductivity of the lattice. At the same temperature, compared with BaMgSi and Ba2Mg3Si4, the lattice thermal conductivity of BaMg(2)Si(2)almost doubles owing to the higher phonon lifetime and group velocities. Our findings highlight considerable potential for thermoelectric applications with a different stoichiometric ratio of Ba/Mg/Si systems due to their low lattice thermal conductivitiesviaintrinsic modulating stoichiometry.