It is 'divine' SLA, per the FAQ.
SKR previously wrote that a WIS-based SLA DC is evidence that an SLA is divine,
but that doesn't necessarily imply that any/all divine SLAs are WIS-based.
CHA is also a Cleric ability stat, as well as the basis of the Oracle with same spell list.
(if anything one should default to spontaneous caster stat, if we use wiz/sor SLAs using CHA as guide)
I tried, but I don't think there is any rule to indicate it would be anything besides CHA.
If you want to boost the DC,
I would take Spell Focus: Necromancy, or anything boosting Fear/Mind-Affecting Spell DCs which apply to SLAs AFAIK.
Or take this as your hint to go for WIS/CHA split build Channel Monster Cleric.
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I really wouldn't expect one. This is one of the most clear-cut rules questions out there. And, as sad as it is to hear, I'm afraid that the staff have better things to do*.
The saving throw (if any) against a spell-like ability is 10 + the level of the spell the ability resembles or duplicates + the creature's Charisma modifier.
Since the dhampir (and associated lineages) say nothing about this working differently from every other spell-like ability in the game, it's safe to assume that they work normally.
So your options are, in order of recommendation:
-Trade it out for an alternate racial trait. Even if your Charisma were magnificent... it's just doom. You can do better.
-Ask your GM to houserule it. This is probably better than asking for a ruling here, in fact; in my experience, most GMs aren't that excited about "I asked the people at Paizo, and now you have to do it this way". (Results may vary, of course.)
-Just accept it. Not that exciting, I know. But sometimes little pieces of a character just don't work.
-Continue to bump this thread forever. I know it worked for the heritages' ability score boosts. Seriously, congratulations on that! I can give you a 99% guarantee that this one won't be as successful, though.
In any case, best of luck with whichever route you choose! ^_^
*It actually wouldn't surprise me if Mr. Seifter did show up, if only because of how clear-cut the answer is.
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HD don't matter for the DC off a spell-like ability. Only the equivalent spell level and Charisma modifier. In this case, the DC for your doom will be 9. 10+1-2. That won't change unless you raise your Charisma or take spell focus or something similar.
They work just like spells. Spell DC doesn't increase with caster level either.