Since you can’t take an Adana kebab as a souvenir, one has to (has to) find a magnet or mug as a souvenir. Recently, I was at the women’s cooperative, Adana Kadın kooperatifleri Birliği, for brunch and it turns out that they also have a shop (one is sitting surrounded by things to buy) so that is my recommendation for where to buy souvenirs.
Adana is famous for its clock tower, orange festival, Roman bridge, and the kebab. This shop, located conveniently in old Adana (just down from the clock tower, on the side of a park, Ziyapaşa Parkı), is a nice reprieve from the heat and bustle. Or cold and wet.
Aside from souvenirs like magnets, they also have handmade items and food for sale. And as I mentioned, you can eat there. The staff are very nice. It is hard to not buy a basket or hammer pants (which is the baggy style that many people wear here).
The other place I would recommend for souvenirs is Starbucks. Sounds odd? The Adana mug is adorable.
There are also other places to find souvenirs but one has to search. Or stick to the main touristy street.