The afterglow emission of gamma-ray bursts (GRBs) is basically well described by synchrotron radiation from fluid shocked by collisions between the jets and the external medium.
However, several afterglow photons with energy from tens of GeV up to 94.1 GeV have been detected by the \textit{Fermi} Large Area Telescope.
Such energy is challenging for the synchrotron radiation from the external shocks and may require another component such as inverse-Compton scattering.

Identifying the responsible emission process in this energy range is important for revealing the central engine and energy dissipation process which causes the bursts.
In the energy range above $\sim 10$ GeV, the sensitivity of the telescope is limited by the signal statistics.
We developed novel photon classes of the \textit{Fermi} Large Area Telescope to recover untapped events with energy above 20 GeV.
Multivariate analysis for rejecting cosmic-ray backgrounds was optimized, and an increase of $\sim 70$\% in the signal acceptance around the peak energy, $\sim 100$ GeV, was achieved.

In these classes, four candidates of photons correlated to GRBs were found. These events arrived much later than the end of the prompt phase.
The observed energy of an event correlated to GRB 090926A at $\sim 4.2\times 10^2$ s after the trigger is 50 GeV. The redshift-corrected energy is 157 GeV. This is one of the highest energy values among GRB photon-like events detected with space telescopes. We estimated the coincidental background detection, and it turned out to be $(2.1\pm 0.3)\times10^{-4}$ counts.
This energy exceeds the synchrotron energy limit for decelerated jets. In this case, another emission component such as inverse-Compton scattering is required.

These results demonstrated the possibility of the new data for scientific studies.