Spouse of Nidaba/Nissaba, goddess of grain and scribes, he is known both as a "door-keeper" and associated with the scribal arts.
Haya's functions are two-fold: he appears to have served as a door-keeper but was also associated with the scribal arts, and may have had an association with grain.
In the god-list AN = dA-nu-um preserved on manuscripts of the first millennium he is mentioned together with dlugal-[ki-sá-a], a divinity associated with door-keepers (An = Anum I 289; Litke 1998). Already in the Ur III period Haya had received offerings together with offerings to the "gate" (Sallaberger 1993: II 38). This was presumably because of the location of one of his shrines.
At least from the Old Babylonian period on he is known as the spouse of the grain-goddess Nidaba/Nissaba, who is also the patroness of the scribal art. From the same period we have a Sumerian hymn composed in his honour, which celebrates him in these capacities (ETCSL 18.104.22.168, see also Brisch 2007: 185-198, with further literature). The hymn is preserved exclusively at Ur, leading Charpin to suggest that it was composed to celebrate a visit by king Rim-Sin of Larsa (r. 1822-1763 BCE) to his cella in the Ekišnugal, Nanna's main temple at Ur (Charpin 1986: 357).
While there is plenty of evidence to connect Haya with scribes, the evidence connecting him with grain is mainly restricted to etymological considerations, which are unreliable and suspect (Weeden 2009: 90-103). There is also a divine name Haia(-)amma in a bilingual Hattic-Hittite text from Anatolia which is used as an equivalent for the Hattic grain-goddess Kait in an invocation to the Hittite grain-god Halki, although it is unclear whether this appellation can be related to dha-ià (Weeden 2009: 93-94).
Haya is also characterised, beyond being the spouse of Nidaba/Nissaba, as an "agrig"-official of the god Enlil. The god-list AN = Anu ša amēli (lines 97-98) designates him as "the Nissaba of wealth", as opposed to his wife, who is the "Nissaba of Wisdom" (Litke 1998: 235).
Attempts have also been made to connect the remote origins of dha-ià with those of the god Ea (Ebla Ḥayya), although there remain serious doubts concerning this hypothesis (Weeden 2009: 98-103; on Ḥayya at Ebla see Archi 2010). How or whether both are related to a further western deity called Ḥayya is also unclear.
In the early periods Haya was mainly worshipped in southern Mesopotamia (Umma, Ur, and Ku'ara). His shrine in Ur may have been located in the Ekišnugal, temple of Nanna, the moon-god. There have been suggestions that Haya was also worshipped at Mari in northern Syria. However, Durand has argued on the basis of the Mari pantheon text that the spouse of Nidaba/Nissaba was in fact dSUMUQAN at Mari, pronounced Šahan, and that the god referred to as Haya at Mari must be a different divinity (Durand 2008: 251).
According to the text of the Neo-Assyrian "Götteradressbuch" (= GAB; Menzel 1981: II T146-166; George 1992: 167-184) Haya had a shrine in the temple of the god Aššur in Assur (Menzel 1981: II 64). Two fragmentary inscriptions from Nineveh mention the planned construction of a temple to Haya by the Neo-Assyrian king Sennacherib (r. 704-681 BCE), although it is not clear where this was going to be located, or whether it was built (Frahm 2002: 1122).
The first attestation of this divine name in writing occurs at Fara (ancient Šuruppak, southern Iraq) in a "school tablet" from the 26th century BCE (SF 77 iv 15). The context is unclear. The god is most frequently attested in the Ur III period, when he had cults attested in Umma, Ur and Ku'ara.
In the Old Babylonian version of the lexical list Ur5-ra I, treating items made of wood, an item bearing his name (giš dha-ià) is listed in association with wooden instruments connected with scribal activity (Veldhuis 1997: 87). For some reason the word for "peacock" is also written using his name (dha-iàmušen) in an Old Babylonian text (Veldhuis 2004: 251-52).
The cult of dha-ià either falls out of use in Babylonia after the Old Babylonian period, if not before, or is not attested. It was revitalised during the Neo-Assyrian period when king Sennacherib (r. 704-681 BCE) planned to build him a temple according to a draught of a foundation document from his reign (Menzel 1981: I 79). He is still characterised as a scribal god. Presumably in this role he presides over a procession of the "gods of Subartu" at a festival in Assur (Menzel 1981: I 139, 243). He also participates in the New Year's Festival at Assur (Menzel 1981: I 79).
Representations of Haya have not been identified thus far.
Mark Weeden, 'Haya (god)', Ancient Mesopotamian Gods and Goddesses, Oracc and the UK Higher Education Academy, 2016 [http://oracc.museum.upenn.edu/amgg/listofdeities/haya/]