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If I’m understanding your question correctly, you’re asking what stat influences max power and power regeneration. If that’s right, then I think I can say that power is not influenced by any stat. Intelligence can help indirectly by increasing the chance of a free skill use, but power shouldn’t be too much of a problem with the right party configuration.
There are, however, items which help with power. Skulls, orbs, and other offhands have a bonus to power regeneration, and rogues can wield bandoliers which grant them +10 to maximum power. Unfortunately, items with power regen are _much_ less common than they were in Book of Dread (probably because the stat was pretty OP in that game, but I digress), so boosts to the stat are limited for characters that aren’t mages/healers. Anyway, hope this helps.
There are also a few items in the game that allow you to generate or steal power when you attack an enemy. Alternatively, you can raise a character’s power regen rate by sticking them in a space adjacent to a cleric that is using the Radiance fighting style.