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Using the density functional theory combined with dynamical mean-fieldtheory, we have performed systematic study of the electronic structure and itsband topology properties of Ce$_3$Pt$_3$Bi$_4$ and Ce$_3$Pd$_3$Bi$_4$. At hightemperatures ($\sim$290K), the electronic structures of both compounds resemblethe open-core 4$f$ density functional calculation results. ForCe$_3$Pt$_3$Bi$_4$, clear hybridization gap can be observed below 72K, and itscoherent momentum-resolved spectral function below 18K exhibits antopologically trivial indirect gap of $\sim$6 meV and resembles densityfunctional band structure with itinerant 4$f$ state. For Ce$_3$Pd$_3$Bi$_4$, noclear hybridization gap can be observed down to 4K, and its momentum-resolvedspectral function resembles electron-doped open-core 4$f$ density functionalcalculations. The band nodal points of Ce$_3$Pd$_3$Bi$_4$ at 4K are protectedby the gliding-mirror symmetry and form ring-like structure. Therefore, theCe$_3$Pt$_3$Bi$_4$ compound is topologically trivial Kondo insulator while theCe$_3$Pd$_3$Bi$_4$ compound is topological nodal-line semimetal.

From Trivial Kondo Insulator Ce$_3$Pt$_3$Bi$_4$ to Topological Nodal-line Semimetal Ce$_3$Pd$_3$Bi$_4$