What does Ātrius mean in Latin?

Ātrius, a proper noun, means “a Roman nomen gentile, gens or "family name"”.

What is the genitive of Ātrius?

The genitive singular is Ātriī. Ātrius is masculine, second declension.

In classical Latin, [ˈaː.tri.ʊs]; in ecclesiastical (church) Latin, [ˈaː.tri.us].

proper noun · masculinesecond declension

Ātrius m sg (genitive Ātriī or Ātrī)

Classical[ˈaː.tri.ʊs]Ecclesiastical[ˈaː.tri.us]

Ā^trĭus, i, m., Quintus Atrius,

I. an officer in Cœsar's army, Caes. B. G. 5, 9.

Maybe from āter (“black”) + -ius.