According to Midrash ha-neʿelam (“The Mystical Midrash”), a work of medieval Jewish mysticism, Arsiel is the entity in charge of Gehenna. He confronts the righteous souls to prevent them from praying for the wicked. Elsewhere, this role of the prince of Gehenna is instead given to Ashmedai, Satan, Abaddon or Samael. While English translations of the Bible often treat Gehenna and Hell interchangeably, the concept has a distinct meaning in rabbinic literature and in kabbalah, closer to the notion of purgatory. Gehenna is a place where a soul resides briefly (at most for a year) and becomes aware of all own deeds, rather than one of eternal damnation.
In Praxis cabulaenigrae Doctoris Johannis Fausti, Magi celeberrimi, a book written in 1612, Aciel (Alciel) is one of seven "planetary spirits," a concept present already in earlier writing related to the character of Faust. These spirits were regarded as servants of Lucifer, and the more famous Mepistopheles has his origin among them. In at least one similar Faustian text, Aciel was specifically identified as the demon associated with the sun.
Megami Tensei seemingly conflated these two unrelated demons. Neither Arsiel nor Aciel appear to have distinctly Mesopotamian origins, and they aren't present in works predating the Middle Ages. Attribution of either of them to "Chaldean" mythology is most likely a misconception rooted in the usage of the term "Chaldean" for anything occult or mystical in European literature.
"According to the mystic Cornelius Agrippa, he is the prince of 'Gehenna', one of the seven levels of hell. His name means 'the sun of night'. He is commonly seen as one and the same with Abaddon and Satan."
—Shin Megami Tensei III: Nocturne compendium
Alciel is first encountered as a boss in the Black Temple of the Amala Temple. Its most dangerous move is Sol Niger, which reduces the Demi-fiend's party to 1 HP, leaving them vulnerable to a physical attack. Alciel will always telegraph this move by spamming Mana Drain the turn before, and the most effective way to prevent an untimely death is to use Tetrakarn or an Attack Mirror in preparation for Sol Niger.
After his defeat, the player can obtain Alciel for themselves. Alciel can only be obtained by evolving an Abaddon at level 74. Alciel also appears as a random encounter in the higher levels of the Tower of Kagutsuchi or the depths of the Fifth Kalpa of the Labyrinth of Amala, but as a member of the Tyrant race it cannot be recruited.
Shin Megami Tensei IMAGINE
Alciel appears as the final boss in the Shinjuku Under Wonder Ground event, accessible only by traveling to the 100th floor. He is supported by Abaddon and Moloch.
Shin Megami Tensei: Strange Journey
"The "Black Sun" who lives in the underworld in Babylonian lore. His original name is Aciel, which the Jews borrowed from a Babylonian god, and called him the "King of Gehenna." But in some Asian faiths, all things are reborn only in darkness, so Alciel is not all bad."
—Shin Megami Tensei: Strange Journey compendium
Shin Megami Tensei IV
Alciel is the creator of the Domain at the Kabuto Shrine in the Ginza region. Defeating him earns the relic Kusanagi Tsurugi, one of the Three Sacred Treasures.
Shin Megami Tensei IV Apocalypse
"The "Black Sun" who lives in the underworld in Babylonian lore. His original name is Aciel, which the Jews borrowed from a Babylonian god, and called him the "King of Gehenna." But in some Asian faiths, all things are reborn only by darkness, so Aciel is not all bad."
—Shin Megami Tensei IV Apocalypse compendium
Alciel can be found in Camp Ichigaya. He can teach Nanashi the Poison Breath, Tetrakarn and Magaon skills through his Demon Whisper. He benefits from learning ailment, Darkness and support skills.