Question: What tribe is the family of Hashim and the Quraysh tribe, who are the dynasties descended from Ali ibn Abi Talib?

Context paragraphs:
Asma bint Umais: Asma bint Umais (Arabic: أسماء بنت عميس‎ ‎ ) was a companion of the Islamic prophet, Muhammad.  She is known for having had the distinct privilege of marrying three companions of the Prophet: Ja'far ibn Abi Talib, Abu Bakr and Ali ibn Abi Talib.

Alids: The Alids are the dynasties descended from Ali ibn Abi Talib, son-in-law of the Islamic prophet Muhammad (see Family tree of Muhammad and Family tree of Husayn ibn Ali).  Shia Muslims consider him the First Imam appointed by Muhammad and the first rightful caliph.

Muhammad ibn al-Hanafiyyah: Muhammad ibn Ali ibn Abi Talib, also known as Muhammad ibn al-Hanafiyyah (15 AH – 81 AH; AD 636 – 700) and surnamed Abu'l-Qasim was an early Muslim leader.  He was a son of Ali ibn Abi Talib, the first Imam and the fourth Caliph.

Husayn ibn Ali: Al-Ḥusayn ibn Ali ibn Abi Talib (Arabic: الحسين ابن علي ابن أبي طالب‎ ‎ ‎ ; 10 October 625 – 10 October 680) (3 Sha'aban AH 4 (in the ancient (intercalated) Arabic calendar) – 10 Muharram AH 61) (his name is also transliterated as Husayn ibn ‘Alī, Husain, Hussain and Hussein), was a grandson of the Islamic "Nabi" (Arabic: نَـبِي‎ ‎ , Prophet) Muhammad, and son of Ali ibn Abi Talib (the first Shia Imam and the fourth Rashid caliph of Sunni Islam), and Muhammad's daughter, Fatimah.  He is an important figure in Islam as he was a member of the "Bayṫ" (Arabic: بَـيـت‎ ‎ , Household) of Muhammad, and "Ahl al-Kisā’" (Arabic: أَهـل الـكِـسَـاء‎ ‎ , People of the Cloak), as well as being the third Shia Imam.

Expedition of Ali ibn Abi Talib: Expedition of Ali ibn Abi Talib may refer to a number of expeditions by Ali ibn Abi Talib including:

Shaheed-e-Kufa: Shaheed-e-Kufa or The Martyr of Kufa or Imam Ali Series (Persian: سریال امام علی‎ ‎ ; Urdu: ‎ ) is an Iranian epic television series focusing on the life of Ali ibn Abi Talib, directed by Davood Mirbagheri, and originally broadcast in 1992 in 22 episodes.  It was subsequently released on DVD, with other editions including one with English sub-titles, and one dubbed into Urdu.  The series covers the events before the caliphate of Ali ibn Abi Talib to his assassination in Kufa, Iraq.

Family tree of Muhammad: This article is about the family tree of the Islamic prophet, Muhammad.  He was known as a member of the family of Hashim and the Quraysh tribe which is ‘Adnani.

Amr ibn Jarmouz: Amr ibn Jarmouz (Arabic: عمر بن جرموز‎ ‎ ) is the man that killed the famous Muslim Sahaba General Zubayr ibn al-Awwam shortly after the Battle of the Camel, while Zubayr withdrew from the army before the battle began due to a hadith that Ali ibn Abi Talib (a) had reminded him with regards to what Muhammad had said to Zubayr: “You will rise up in a battle against Ali ibn Abi Talib”.

Malik al-Ashtar: Malik Al-Ashtar (Arabic: مالك الأشتر‎ ‎ ) (also known as Malik bin al-Harith al-Nakha'i) was one of the most loyal companions of Ali Ibn Abi Talib, the cousin of the Islamic prophet Muhammad.  Malik al-Ashtar became a Muslim during the time of Muhammad and since then remained an avid and loyal supporter of Muhammad's progeny and Hashemite clan.  He rose to a position of prominence during the caliphate of Ali Ibn Abi Talib and participated in several battles, such as the Battle of Jamal and Siffin.

Sha'baniyah Munajat: The Sha'baniyah Munajat (Persian: مناجات شعبانیه‎ ‎ ) is a supplication attributed to Ali ibn Abi Talib, the first Shia Imam, that invoked in the Sha'ban month.  The supplication was narrated by Ibn Khalawayh and is mentioned by Abbas Qumi in Mafatih al-Janan, Sayyed Ibn Tawus in Eqbal al-a’mal, and Muhammad Baqir Majlesi in Bihar al-Anwar.  In the Mafatih al-Janan, the Munajat mentioned at Sha'ban month prayers section.  This supplication known as a monologue of Ali ibn Abi Talib with his God, Allah.  In the supplication, Ali emphasizes on God's generosity and called Allah as creator and infinite of human.  Ali advised to recite the Du'a with presence of heart.

Supporting paragraphs: Alids Family tree of Muhammad
Answer: Adnani