I remember this being asked during one of the Rune Fencer AF quests:
https://ffxiclopedia.fandom.com/wiki/Legacies_Lost_and_Found
So if Ignis increases resistance against Ice and deals fire damage, so I think the answer to your question is "Barblizzara" and "Barparalyzra" (and of course, Ignis, and froms songs, you can cast Ice Carol 1 which takes priority over Ice Carol II, if you can't cast both songs).
(It is worth to note, I don't think anyone can accurately test the potency of the bar-status effect spells, like Barparalyze, but I try to be optimistic and assume that it's not terrible).
As a result, when a fight has a specific status effect that I wan't to avoid, I use the above rational.