What would the possessive pronoun of the 'zȳhon' stem be in the place of 'jāhe' here? Zȳhe? Also, when does one use zȳhon and when jāhon, as both seem to stand for 3rd person singular?
It should be jāhe here.
Jāha is used for agreement with solar/lunar nouns (like muña).
Zyyha is used for agreement with terrestrial/aquatic nouns (like lōgor)
It's actually the opposite:
Which stem to use is determined by the possessor, rather than the possesee:
Zȳha and its declined forms are used for solar and aquatic nouns (like zaldrīzes),
Jāha and its declined forms are used for aquatic and terrestrian nouns (like qintir, as in this case).