use of -gha verses -ga in name spelling

[TonyM]

In my search of the online Italian genealogy records, I've run into many cases where a name is spelled using both a -ga ending and a -gha ending. My question is: is there a basis for this in historical Italian spelling (orthography) rules? I know that h is used to signal the hard g sound when i or e follows. But was there perhaps a historical rule, for the letter a, i.e., gha?

Actually, I'm interested in any info at all on whether this -gha vs. -ga spelling is just a mistake made by semi-literate record keepers, or has some more solid basis. This could give insight to how ancestors pronounced my last name and its origins.

If you type "gha" into the Cognome box on "Trova i nomi" page of the Antenati site you find many names ending in -gha. Often, the name is indeed spelled with -gha in the linked document, but then if you look at the corresponding index entry the name is spelled with a -ga ending.

Here's one example, with a screenshot from linked the death record first and below that a screenshot from the corresponding index entry:

And here's another example where the document (top) has the -ga ending, but the corresponding index entry has the -gha ending

I originally posted a question in an Italian language forum, but then I realized genealogy experts here may know more about this topic.

Thanks for your help.