This came up in a discussion.

A's ball at their 1. A32 running out of the end zone when B37 swats at the ball knocking it backwards into the end zone and out of bounds over the endline.

Safety or touchback? Why?

You don't say where the ball was when it was fumbled but it's a safety either way. If the fumble was in the EZ, A forced the ball into the EZ by either carrying it or snapping it into the EZ. If the runner was out of the EZ when he fumbled the ball, the batting of the ball is not a new force, and A still forced the ball into the EZ. (8-5-1)

Safety.

The way the play is described B37 forces the ball into A's end zone with his bat. That would seem to mean a touchback. However, the ball is in A32's possession, and when A32 loses possession (regardless of how he does so), it's a fumble. So the force into A's end zone was A32's fumble. Hence a safety.

Safety,

B's bat would not be considered a new force as A had possession.