If I hold a BF at the beginning of my turn, then move out and go back with a unit on it, does it trigger the conquer ability of my unit?

No, moving a unit back to a battlefield you already held earlier in the same turn does not trigger your unit's "When I conquer" ability.

According to Rule 465, a player may only score (either by Hold or Conquer) once per battlefield per turn. Because you already scored that battlefield via a "Hold" effect during your Beginning Phase, you have reached the scoring limit for that location for the turn.

As clarified in FAQ #3369 and FAQ #1699, "Conquering" is a subset of scoring; if you have already scored a battlefield—regardless of the method—you cannot perform a conquer action there for the remainder of the turn. Consequently, any "When I conquer" abilities on your units will not trigger when you return to that battlefield.