Related (yet different): What is the source of a Paladin's spell-casting ability?
Related (strongly): What are the impacts of changing a Ranger's spellcasting ability? (I don't know if everything that's said about the Ranger is applicable to the Paladin)
My player wants to create (L1) an investigator-type paladin (of the Inquisition) and asked that Intelligence becomes the character's spell-casting ability and, if possible, also class features ability (e.g. Lay on Hands).
PHB states that:
Charisma is your spellcasting ability for your paladin spells, since their power derives from the strength of your convictions. You use your Charisma whenever a spell refers to your spellcasting ability. In addition, you use your Charisma modifier when setting the saving throw DC for a paladin spell you cast and when making an attack roll with one.
Since they are not asking for extra skills than the ones already provided by race, class & background, i.e. Paladins can pick from two Charisma skills (Intimidation, Persuasion) and one Intelligence skill (Religion) at character creation, I don't see any system-unbalancing issue in this approach.
Also, I suppose that Intelligence save proficiency should be awarded instead of Charisma on character creation.
To be clear, my issue is not the fluff of "the strength of convictions" (I'll probably trump it as "rigorous reasoning" ala Sherlock Holmes) but whether the PC becomes over/under -powered, compared to the normal Charisma-based option, over the short and long run.
In case it is relevant, it is a Human-only (for PCs) campaign, with options only from PHB (feats included) excluding multi-classing.