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My German is currently not good so please use English so I can understand
according to this link https://en.wikipedia.org/wiki/German_nouns#Declension_for_case
II: Personal names, all neuter and most masculine nouns have genitive case -(e)s endings
It said "all neuter" that mean including neutral n-nouns but
III: Masculine and neuter n-nouns take -(e)n for genitive, dative and accusative
so what exactly is neuter n-nouns in genitive case
I think the Wikipedia page is wrong about point III. According to the German version of the same article
Anmerkung: Hier gibt es keine Neutra
which is literally saying that in group III there are no neuter nouns.
You asked »what exactly is neuter n-nouns in genitive case«, and there is exactly one German word that is neuter and an n-noun (all other n-nouns are masculine, and no other neuter noun is an n-noun):
(the heart)
Eines der wichtigsten Organe des Menschen ist das Herz.
Ich spüre das Pochen des Herzens.
(Only as medical term: Hier befindet sich der Vorhof des Herzes.)
Schenke deine Aufmerksamkeit mehr dem Herzen.
but also:
Schenke deine Aufmerksamkeit mehr dem Herz.
Dr. Frankenstein to his servant: »Igor, reiche mir das Herz herüber.«
Die Herzen der Zuschauer schlugen höher.
Die Zubereitung der Herzen bereitete dem Koch große Freude.
Erich gab den Herzen auf seinem Bild eine besonders kräftige Farbe.
Seine Rede erreichte die Herzen der Zuhörer.
Unfortunately, there is no rule for it, some nouns take s others es or ens or en.
they are classified by categories , take a look at the following link:
http://www.dietz-und-daf.de/GD_DkfA/Gramminfo/txt_MII1/Nominal-Flexion%20Q1%20Info.pdf
