Cub Driver writes:

The aircraft was known as the Navy Type 0 Carrier Fighter Model 22A
when long-barreled 20-mm Type 99 Model 2 Mk 3 cannon were installed
(Joe Baugher).

What puzzles me about the designation is that Japanese doesn't use the
alphabet. Must be a translation of something else.

Yes, in English we often use a,b,c etc. for ordinal counting. As you
probably know, the Kou, Otsu, Hei, Tei, etc 1-set ordinal counting is
from the old Chinese counting method (koyomi), in which two
characters, one going through a cycle of 10, the other through a cycle
of 12, were used to describe the year and by the same method also the
day. A total cycle of years therefore was 120, days also 120 (thus
three or more occurrences of the same koyomi day in one solat
year). Therefore substitute a,b,c,d etc as quite adequate. For ships,
you can find the same attributes in the Kaibokan (escorts): Types Kou,
Otsu, Hei, etc.

Also, the "A" doesn't make any sense where it's situated. What does it
modify, the first 2 or the second?

Good question, as far as I know it means a minor modification, so
neither of the digits are modified: it refers in aircraft basically to
armament and other equipment changes.

I notice that in the translation of Hata & Izawa's Japanese Naval
Aces, there is a reference to Zero Model 52 Type C, which strikes me
as more logical. (Again, "C" would be a translation of some other
term.)

C corresponds to Hei (i.e., Third)

Baugher's narratives on Japanese aircraft often don't track Japanese
accounts.

Mmm, I don't blame him, given the prodigious output on that website,
it is only natural that the most common and not necessarily best
references were used!

--
G Hassenpflug * IJN & JMSDF equipment/history fan