You can imagine it this way: prepare damage blocks above each adventurer according to the trap text, as if there were no thief or paladin (but do not assign damage yet). Now remove one block for each trap icon in the party, starting with the blocks prepared for the first adventurer, etc. Assign the remaining damage, if any is left. The prevented damage is not dealt.

No matter how much damage is prevented (even if all damage is prevented), the special effect of the trap (no conquering, no spellcasting, skipping the Healing Step, extra damage from poison) is never prevented.

This works the same way every round, regardless of whether some damage was prevented in previous rounds, as long as there are any surviving adventurers with the anti-trap skill.