What word did Jesus use for God in Aramaic?

Matthew 27: 46-47 indicates that both Eli and Elia (the Aramaic version of Elijah) are rhyming words because the bystanders misunderstood Jesus' cry: "And about three o’clock Jesus cried with a loud voice, “Eli, Eli, lema sabachthani?” that is, “My God, my God, why have you forsaken me?”. When some of the bystanders heard it, they said, “This man is calling for Elijah.”

In fact, “ì” in Eli is pronounced as “y” as in daily (and not as “y” as in shy) and “ìa” in Alia is pronounced as “ìa” as in media. So, Jesus called God: Eli.

Incidentally, in old Malayalam (a language of southern India) versions of the Gospels which had directly been translated from the Syrian language (written form of Aramaic), used the word “Eli” in the cry of Jesus at the cross and the name Elia for prophet Elijah. Thus, the confusion of the bystanders is best explained. So, Jesus called God the Father as “Eli” in Aramaic.

Eloi Eloi lama sabachthani?" is Greek transliteration of Aramaic words. If it was Hebrew, then azabthani would have been used instead of Aramaic word "Sabachthani."

Check this link for Hebrew NT of Mark 15:34.

In Hebrew, "Eloi Eloi lama sabachthani?" will become "Eliy ‘Eliy lamah `azab’taniy?"

The spoken language of first century Israel was Aramaic. Not Hebrew or Greek. Check this link for more information.

Why didn't the Jews understand "Eli, Eli, lama sabachthani"?

The word for God in Aramaic was Eil and Elaha (also written as Alaha). In first century Judea, they used both "Eil" and "Elaha" for God. But in Samaria, Galilee, Lebanon, and in Syria during first century, they mostly used Elaha (also written as Alaha).

Since Jesus Christ grew up in Galilee, he would have used Elaha.

If you check Matthew 27:46 of Aramaic Peshitta (Aramaic NT), then you will see "Eil Eil." This was somewhat clumsily transliterated by Greek scribe as "Eli Eli." Sometimes Greek scribes have difficulty transliterating Aramaic words into Greek. For Example, Aramaic words "Khqel Dama" in Acts 1:19 is transliterated as "Akeldama" in Greek.

YHWH is Hebrew. But Jesus spoke Aramaic. Not Hebrew.

In first century Israel, Jews used Aramaic Old Testament known as Peshitta Tanakh.

The information about Peshitta Tanakh is available here.

YA (in Aramaic OT and Aramaic NT Peshitta) is the Aramaic form of Hebrew "YH" in "YHWH." Because of this, Hebrew name "Yehochanan" becomes "Yochanan" in Aramaic. Another example is Hebrew name "Yehonathan" becomes "Yonathan" in Aramaic and Hebrew name "Yehoseph" becomes "Yoseph" in Aramaic.

For Respect, "YA" is addressed as "MarYA" (Master YA) in Aramaic OT, in Aramaic NT, & in First century Israel.

The name of God in the Hebrew Bible is YHWH, pronounced Yahweh or Jehovah.

There are many words used in the Hebrew Bible for the word 'God' (not the name of God), such us El (god), Elohim (god, plural form), El Shaddai (god almighty), Adonai (master), Elyon (highest) and Avinu (our father) are regarded by many religious Jews not as names, but as epithets highlighting different aspects of YHWH and the various 'roles' of God (source).

From Wikipedia article on Allah,

The term Allāh is derived from a contraction of the Arabic definite article al- "the" and ilāh "deity, god" to al-lāh meaning "the [sole] deity, God" (ὁ θεὸς μόνος, ho theos monos). Cognates of the name "Allāh" exist in other Semitic languages, including Hebrew and Aramaic. Biblical Hebrew mostly uses the plural form (but functional singular) Elohim. The corresponding Aramaic form is ʼĔlāhā ܐܠܗܐ in Biblical Aramaic and ʼAlâhâ ܐܲܠܵܗܵܐ in Syriac as used by the Assyrian Church, both meaning simply 'God'.

Elohim is not the name of God, it is simply 'God' in Hebrew. Many languages have some similarities because many of them share the same origin. 'God' in English, 'Elohim' in Hebrew, 'Elaha' in Aramaic, 'Alaha' in Syriac etc. but the name of God in the Bible is YHWH, not Allah as some Muslim scholars may try to relate them. Hence, the God in the Bible is YHWH and the god in the Qu'ran is Allah. The most specific Hebrew name for God is YHWH, also mistakenly referred to as Yehovah, meaning self-existent and eternal. YHWH is rooted from ‘Hayah’, the to be verb, which is from ‘Hava’, to breathe, or to be, which connects to ‘Ayil’. Finally ‘Ayil’ leads us back to ‘El’, which is the root of all the Semitic names for God. YHWH is spoken aloud on rare Jewish celebrations as just “Ya.” Jews often replaced the actual name of God for Adonay (Lord) orally and in their written scripts.

For instance, see this typical translation of Exodus 20:7

Thou shalt not take the name of YHWH thy Elohim in vain; for YHWH will not hold him guiltless that taketh his name in vain.

Jesus spoke Aramaic many times during His ministry, hence, he must have used the word 'Eli' or 'Elaha' (ʼĔlāhā) many times to say 'God'. For instance, while Jesus was on the cross, He cried out in Aramaic.

About three in the afternoon Jesus cried out in a loud voice, “Eli, Eli^[a], lema sabachthani?” (which means “My God, my God, why have you forsaken me?”) [Matthew 27:46, NIV]

_{[a] Some manuscripts Eloi, Eloi}

The normal generic word for God is "alaha"/"aloho" (ܐܠܗܐ), which is linguistically related to the Hebrew word for God "elohim".

The translation of the tetragrammaton, YHWH, on the other hand, is "maria"/"morio" (ܡܪܝܐ), usually decomposed as mar-yah, Lord-Yah ("mar", lord, also being used by syriac speaking churches as a title for saints/doctors of the Church: "mor Ephrem" = Saint Ephrem). (Note: this word has nothing to do with the proper name Maria, coming from the Hebrew Mariam)

To answer your question, Jesus would almost certainly have used one of the two, or both at the same time as it is commonly done in Syriac: Maria Alaha.

Last remark: The arabic word Allah, used also by Arabic Christians, is no more no less related to the Aramaic Alaha than to the Hebrew Elohim. The three share a common linguistic root, which is nothing exceptional, so no point being dragged on sterile arguments concerning this point.

Concerning the cry on the cross (quote from Psalm 22:1), the Peshitta (the earliest christian Aramaic translation) translate it using the word alaha, with the first person possessive suffix -i : alahi (ܐܲܠܵܗܝ ܐܲܠܵܗܝ ܠܡܵܢܵܐ ܫܒܲܩ̣ܬܵܢܝ̱ ). The original Hebrew Psalm used "Eli". Since the scriptor of the Greek gospel may not have been fluent in Aramaic, or used to transliterate Aramaic with Greek characters, it may be expected that the transliterations are approximates, hence a possible : eloi/alohi confusion.