Here is something from:
A Dictionary of Ancient Near Eastern Mythology
by Gwendolyn Leick,
originally posted
hereDoesn´t say anything about the genealogy tho.
"
AššurAssyrian god, the eponymous deity of the capital Aššur who became the
national god of Assyria.
The origin of the name is unknown. He seems to have been a local
mountain god of the Semitic population of northern Mesopotamia (bel
šaduabeh) and known as such from texts since the Ur III period. With the
rise of the political power of Assyria, Aššur was promoted to a supreme
rank among the gods, taking on the characteristics of several other
gods, such as Enlil, Anu and Šamaš. This process recalls the elevation of
Marduk in Babylon. An Assyrian version of the Enuma Eliš replaces
the name of Marduk by Aššur, who was at the same time equated with
Anšar. The worship of Aššur survived in northern Mesopotamia until
the third century AD.
The Assyrian monarch had a special relationship to this god whom he
served as the first priest of Aššur and who was directly responsible for the
exercise of kingship, in analogy to the role of Anu and Enlil in Babylon.
Aššur seems to have had no official consort before the reign of
Sennacherib (7th C BC), when Ninlil appears as his wife. On the other
hand, Ištar of Aššur or of Nineveh are also mentioned as wives of the
great Assyrian god.
His iconographical image, which appears on various Assyrian reliefs
and obelisks, shows a winged sun-disc containing a bearded deity holding
a bow.
Tallqvist 1932; Ebeling, RLA I 1932, 196–8; Dhorme 1969; Mayer 1997"
from the same book
"
Ištar Aššuritum, wife of Aššur, the national god of Assyria."
"In Assyria, Ninlil became the wife of the national god Aššur."
I just checked the RlA1, but there is no information
apart from the fact the we know nothing about his parents.