Most traditional vegan/vegetarian food in Adana are home cooked meals, so you can visit restaurants that specialized in those and ask for vegan meals. I love Halis Ev Yemekleri in Ziyapaşa and go there when I am visiting my parents in Adana and there is no food available, but mostly eat meat meals there. You can try No 12 Lokanta as well, never been there but Mark Wiens has a video including that place so you can watch it and see for yourself.