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?
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.
Hierarchial taxonomy terms should not be unique on different parents.
You can perform a Hierarchial Run to solve your model for multiple objectives simultaneously. (IBM)
Hierarchial Coassembly of a Cyanine Dye in Poly(vinyl alcohol) Fibrous Films by Electrospinning (ACS Journals)
Hierarchial Task Analysis (book by) Andrew Shepherd