I read this short SF story in around 2008, but cannot remember the title and only vaguely remember the story. I'm not able to find the story on any search site, so I am asking about it here.
I have checked other answers, and the story is not "Let's go to Golgotha!", or "The Didymus Contingency".
A time traveller has to go back to the past for some work. The time machine malfunctions and he ends up in Israel in the time just after crucifixion. As soon as people see him coming out of a tomb, they run after him. He is surprised as to how people recognize him. He finds his way back to the time machine and returns to his time.
He tries another attempt to go back to the past. This time he ends up a little earlier. He gets stuck in the time there, and lives his life teaching people, until he is crucified.