For Turks:
National Epic should be Ergenekon or
Orkhon Inscriptions. Orkhon Inscriptions explain the deeds of Bilge Khagan and foundation of Second Turkish Khaganate, it's more like a biography than a legend. But if a legend is preferred then it should be
Ergenekon*. It explains the foundation of Turkic Khaganate.
Dede Korkut Stories is not a single epic, it's just a collection of myths, so I don't think it's suitable for an individual "epic". But if Poetic Edda is considered an epic then Dede Korkut would be okay as well.
For the heroic epic, it's definitely
"The Legend of Oghuz Khagan", Köroğlu might be suitable for Ottomans but not too much for the Central Asian Turks.
*:Civ funfact, Doviello in FFHII share almost the same origin story with Turks (Sons of Asena entry).
For the Ottomans:
Dream of Osman is not even a proper epic, so I think there should be a better alternative. But the problem is Ottoman literature was written in Farsi/Arabic so noone actually reads them in Turkey and they are not very popular, but we can pick
Masnavi if that is okay.
If non-epic verbal literature is okay
Nasreddin Hodja has the biggest influence in Turkish culture in my opinion.
If republican era is okay then "Kuvayi Milliye Destanı" by Nazim Hikmet would be my candidate. I couldn't find any English sources but Nazim Hikmet is definitely the most famous Turkish poet and this is a relatively known epic in Turkey.
For the heroic epic, Köroğlu Destanı is a very good choice.
These are my suggestions for the quotes:
Orkhon Inscriptions:
To the south the Chinese people was our foe, to the North Baz kagan and the people of the Nine Oguz’s were our foes; Kirghiz, kurikans, Thirty Tatars, Kitays and Tatabis — they were all hostile to us; all these had my father, the kagan, fight*. Forty-seven times he went campaigning, and fought in twenty fights. By the will of Heaven we took from them that had a kingdom their kingdom, and them that had a kagan we robbed of their kagan; he made the foes to keep the peace, and made them bow their head and bend their knee.
*:Not sure about the grammar tbh, I don't know this structure in English. But it's like they made his father fight.
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Oghuz Khagan:
"I have become your Khan;
Let's all take swords and shields;
Kut (divine power) will be our sign;
Gray wolf will be our
uran (
battle cry);
Our iron lances will be a forest;
Khulan will walk on the hunting ground;
More seas and more rivers;
Sun is our flag and sky is our tent."
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Köroğlu Destanı - Köroğlu Legend:
"I'm the sword of God, I'm seeking the just *
I challenge the Shah, and the Padishah
Awake from your sleep and you'll join me"
*: God and just are homonymous in Turkish, so it sounds better in Turkish
Quote that is mentioned in first page is also okay imo.
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Not sure about Masnavi, don't know too much about it.
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Nasreddin Hodja:
Mulla had lost his ring in the living room. He searched for it for a while, but since he could not find it, he went out into the yard and began to look there. His wife, who saw what he was doing, asked: “Mulla, you lost your ring in the room, why are you looking for it in the yard?” Mulla stroked his beard and said: “The room is too dark and I can’t see very well. I came out to the courtyard to look for my ring because there is much more light out here.”
Well, Nasreddin is just a common character in many jokes and these are neither epics or poems. but he is the most popular character in Turkish literature.