The search field in Zotero will default to Title, Creator, Year (it says in light grey font). You can toggle it to different modes by clicking on the small arrow at its left.

OK. I'm a little puzzled by that 2008 reference -- that persists when you refresh the document?

Next up, we'll want to narrow the document down. You'll effectively want to run a version of this:
https://www.zotero.org/support/word_processor_plugin_troubleshooting#debugging_broken_documents

With a focus on 8.) (though do run through the others, which may fix this)

It's a little different here, though, because you'll need to check the bibliography all the time. Essentially you'll want to split the document in two, insert bibliography and check if there's a reference to Carmel and Harlock that shouldn't be there in the bibliography, i.e. either theres both 2008a and 2008b, or there is _any_ reference where none is cited in the document.
If one half is working correctly, keep narrowing things down further with the other half.

I don't work for Zotero and my hours aren't regular. I drop by when I have time US Eastern Time

This follows your advice yesterday and I’ve continued using the same document.

There are three Carmel and Harlock citations in this document, which I’ve split into two halves and then split the second half into two quarters. These are the results:

FIRST HALF
One Citation: Show Editor 2008 and bibliography 2008. But another pair of duplicates has appeared, though their citations do have a and b, despite their being from only one reference.

THIRD QUARTER
One Citation: Show Editor 2008 and bibliography 2008. But another pair of duplicates has appeared, though their citations don’t have a or b.

FOURTH QUARTER
One Citation: Show Editor 2008a but bibliography is both 2008a and 2008b

I don’t know whether this means anything yet. Since there are only three citations in the document, I’m unsure how I can split this further. Can you please give guidance on what I should do for next steps?

To conclude this: huckfield and I took this offline by e-mail. What we found were that there we hidden stray references in the document, most likely caused by using Show Editor (that was the case for the one I looked at more closely, but there may be other causes). The document also had some RefWorks references in there, which may have caused problems for Zotero, though we don't know that.

If someone finds themselves in a similar situation, the best advice I can give would be to try to prevent this from happening by
1. Avoiding to manually edit citations or use Show Editor
2. Merge Duplicates rather than deleting them in your library.

If you find yourself with a document with stray a/b/cs and replacing them from your library as described doesn't fix it, a useful way to troubleshoot can be to show field codes (alt+F9) and search for the authors of references that are falsely duplicate in the bibliography as well as for items that may have different uris although they're the same item. This is all rather technical (and the field codes look pretty intimidating) and it's certainly not intended to be necessary ever.

Ok i have the same problem and I follow your discussion... i not courageous like you, after 3 hours I decid to do it manually

it is a NIGHTMARE

edit: mylenetesson's original thread is here: https://forums.zotero.org/discussion/78721/inserer-une-ref-sans-a-et-b-a-cote#latest
follow-ups should go there.