The Ottoman Ring is the eighth treasure that can be found in Uncharted 2: Among Thieves.
The Ottoman Ring is found in Chapter 2 - Breaking and Entering. It should come as no surprise that you'd find Ottoman artifacts in Turkey, and one of them is around you directly after the brief sequence of them dodging being seen from the windows by the guards inside. Move forward and go up a short staircase to your left. You're now in what appears to be some sort of supply room, with unused artifacts and exhibits all around you. If you think there just has to be a treasure around here somewhere, then you'd be right. Swing rightward and move towards the large wooden door you'll need to use to continue. When you reach it, turn right and the treasure is in the corner, grab it before proceeding through that door.