In this work, random telegraph signal noise (RTN) is comparatively investigated in HfSiON and HfLaSiON n-type field effect transistors (nFETs) for further understandings on impacts of La incorporation in high-k devices. Constant bias RTN (cRTN) and transient RTN (tRTN) are characterized in detail, including carrier trapping time constants, gate bias couplings of time constant ratios, and carrier trapping/de-trapping induced channel current fluctuations or recoveries. On the one side, in comparison to HfSiON nFETs, it is observed that there exist fewer low energy traps by La incorporation, as well as smaller channel current fluctuations. On the other side, using tRTN measurements, more traps with high energies are observed in HfLaSiON nFETs, which could explain worse PBTI properties in HfLaSiON nFETs under high electric field. Underlying physical mechanisms are also discussed.