If I hold a battlefield and then combat happens and we kill each other, then if I go to that battlefield does that trigger Conquer?

No, moving back to that battlefield will not trigger "When I conquer" abilities, nor will it count as a conquest action.

According to Rule 465, a player may only score each battlefield once per turn, regardless of whether that score was achieved by Holding (at the start of your turn) or by Conquering. Since you already scored that battlefield by holding it during your Beginning Phase, you have already reached the scoring limit for that battlefield for the rest of the turn.

As clarified in RiftJudge FAQ #3558 and FAQ #6745:

• Conquering is a specific method of scoring.
• If you have already scored a battlefield (via Hold or Conquer) earlier in your turn, you cannot score it again.
• Because you cannot score the battlefield again, you cannot perform the "Conquer" action, and consequently, any "When I conquer" abilities will not trigger.

While you can still move units back to the battlefield and potentially retake control of it, you do so without triggering any conquer-based effects or gaining additional scoring points from that location for the remainder of the turn.