Question: Which Halime Hatun son was the leader of the Ottoman Turks and the founder of the Ottoman dynasty?

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Battle of Aspindza: The Battle of Aspindza (Georgian: ასპინძის ბრძოლა ) was fought on 20 April 1770 between the Georgians, led by king of Kartli-Kakheti Erekle II, and the Ottoman Empire.  The Georgians won a victory over the Turks.  The Georgian king asked Russian general Totleben for aid in the battle of Aspindza; in return Erekle would do his best to cultivate good relations with Russia.  General Totleben agreed to help.  As soon as the small army of Erekle and large army of Totleben were about to meet and merge, Totleben and his army changed course and returned to Russia.  Totleben's plan was to let the Ottoman Empire completely destroy the Kartli-Kakhetian army along with the king.  Russia, then, could easily incorporate the kingdom into the country.  Erekle, along with his outnumbered army, was devastated.  Nevertheless, the morale of the Georgians managed to override the Ottoman Turks, and the battle ended with a Georgian victory.

Hatice Halime Hatun: Hatice Halime Hatun (Ottoman Turkish: خديجة حليمة خاتون‎ ; before 1415, Devrekani – after 1500) was the wife of Sultan Murad II.

Hüma Hatun: Hatice Âlime (Halime) Hüma Hatun (Ottoman Turkish: هما خاتون‎ , 1410 ‒ September 1449) was the fourth wife of Ottoman Sultan Murad II and mother of Mehmed II.  She was a slave girl.  Nothing is known of her family background, apart from the fact that an Ottoman inscription (vakfiye) describes her as "Hātun binti Abdullah" (Daughter of Abdullah); at that time, people who converted to Islam were given the name "Abdullah" meaning "Servant of God", which is evidence of her non-Muslim origin.  Her name, "hüma", means "bird of paradise", after the Persian legend.  There are two theories on her origin: She was a romanian named Stella; She was Serbian, some sources saying that she was a princess from the Principality of Zeta and a relative of Đurađ II Balšić.  S. Runciman and Ilber Ortayli support that she was of Slavic descent.  She died in September 1449 in Bursa.

Ottoman dynasty: The Ottoman dynasty (Turkish: "Osmanlı Hanedanı" ) was made up of the members of the imperial House of Osman (Ottoman Turkish: خاندان آل عثمان‎ "Ḫānedān-ı Āl-ı ʿOsmān").  Also known as the Ottomans (Turkish: "Osmanlılar" ).  According to Ottoman tradition, the family originated from the Kayı tribe branch of the Oghuz Turks, under Osman I in northwestern Anatolia in the district of Bilecik Söğüt.  The Ottoman dynasty, named after Osman I, ruled the Ottoman Empire from c. 1299 to 1922.

Halime Hatun: Halime Hatun (Ottoman Turkish: حلیمه خاتون‎ ) was the wife of Ertuğrul, and the mother of Osman I, the founder of the Ottoman Empire.

Treaty of London (1827): The Treaty of London was signed by the United Kingdom, France, and Russia on 6 July 1827.  The three main European powers had called upon Greece and the Ottoman Empire (Turkey) to cease hostilities that had been going on since the Greeks had revolted against Ottoman rule on 6 March 1821.  After years of negotiation, the European allied powers had finally decided to intervene in the war on the side of the Greeks.  The allied powers mainly wanted this treaty to cause the Ottoman Empire to create an independent Greek state.  It stated that while the Ottoman Empire should recognize the independence of Greece, the Sultan would be the supreme ruler of Greece.  The treaty declared the intention of the three Allied powers to mediate between the Greeks and the Ottoman Turks.  The base arrangement was that Greece would become a dependency of Turkey and pay tribute as such Additional articles were added to detail the response should the Turkish Sultan refuse the offer of mediation and continue hostilities in Greece.  These articles detailed that the Turks had 1 month to accept the mediation or that the Allied powers would form a partnership with the Greeks through commercial relations.  Measures were also adopted that if the Ottoman Sultan refused the armistice, the Allies would use the appropriate force to ensure the adoption of the armistice.

Persian embassy to Europe (1599–1602): The Persian embassy to Europe (1599–1602) was dispatched by the Persian Shah Abbas I in 1599 to obtain an alliance against the Ottoman Empire.  The Persians had then been at war with the Ottoman Empire for more than a century, and so decided to try to obtain European help against the Ottomans.  Besides the territorial antagonism of the Ottoman and Persian realms, there was also strong religious antagonism, as the Persians proclaimed Shiism against the Ottoman Empire's Sunnism.  The objective of the mission was to establish a European–Persian alliance against the Ottoman Turks.  These Persian efforts at rapprochement with Europe followed the Persian defeat against the Ottoman Empire in the Ottoman–Safavid War (1578–1590).

Osman I: Osman I or Osman Gazi (Ottoman Turkish: عثمان غازى‎ "ʿOsmān Ġāzī"; Turkish: "I. Osman, Osman Gazi, Osman Bey, Osman Han, Osman Alp" ; died 1323/4), sometimes transliterated archaically as Othman, was the leader of the Ottoman Turks and the founder of the Ottoman dynasty.  He and the dynasty bearing his name later established and ruled the nascent Ottoman Empire (then known as the Ottoman Beylik or Emirate).  The state, while only a small principality during Osman's lifetime, transformed into a world empire in the centuries after his death.  It existed until shortly after the end of World War I.  Historians commonly mark the end date at the abolition of the sultanate in 1922, or the proclamation of the Republic of Turkey in 1923, or the abolition of the caliphate in 1924.

Malhun Hatun: Malhun Hatun (died November 1323, other names "Mal Hatun, Mala Hatun, Kameriye Sultana") was the first wife of Osman I, the leader of the Ottoman Turks and the founder of the dynasty that established and ruled the Ottoman Empire.  She was the mother of the next and second ruler of the Ottoman State, Orhan.

Mehmed Orhan: Mehmed Orhan (Ottoman Turkish محمد اورخان; 11 July 1909 – 5/12 March 1994) was the 42nd head of the Ottoman dynasty from 1983 to 1994.  He succeeded as head of the Ottoman dynasty on 9 December 1983, following the death of Ali Vâsib.  If reigning, he would have been styled as Grand Sultan Orhan II.

Supporting paragraphs: Halime Hatun Osman I
Answer: Osman I