The accident occurred when five persons rushed to board the Maurya Express and fell on the track, railway officials said.
While three of them were run over, two others were injured.
The station falls under Barauni section of Samastipur Division.
The deceased were identified as Prabhat Chaudhury (35), Anju Devi (30) and her son.
The injured were admitted to Dharahara Barauni Railway Hospital, they said.