I've found one reference that says hierarchial is an alternative form of hierarchical, but it's an unreferenced resource. Some wiseacre wrote a bug fix for my software saying hierarchical was the only spelling of the word and I'd like to prove said wiseacre wrong. So, can someone crack open the Oxford English Dictionary with the tiny print and help me out?
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Neither Oxford Dictionaries nor the OED has an entry for hierarchial, but the OED does have entries for hierarchal and hierarchic as well as hierarchical. This, however, is not to say that hierarchial doesn’t exist.
Between "a word" and "not a word" is a no-man's-land where the casualties of past flame wars lie bleeding.
That said, your proposed variant is wobbling on two weak legs, not only is the -ial unusual here at best, but the heir- is generally considered a typo when it happens.
You might be able to show it meets the condition of at least having some use, but it wouldn't be advisable to use.
For that matter, I can find jerarchy, jerarchye, cherarchy, ierarche each mentioned in the OED as having been forms used for hierarchy, but that doesn't make any of them spellings to use in most modern contexts.
Wiktionary lists hierarchial as an alternative form of hierarchical. (NB spelling)
Google tries to correct to hierarchical, though.
Interestingly, the NIH (which should particularly know the difference between hierarchical and hierarchial) lists their "Office of Acquisition and Logistics Management" Hierarchial Structure. This might be more common in the Sciences and technology.