Straight double quotes on Bluetooth keyboard
Which key does what depends on the Input Source you are using (not your hardware). These are activated  in System Preferences/Keyboard/Input Sources.  To see the current mappıng, use Keyboard Viewer. 

Your keyboard is Turkish Qwerty PC.  If you make that your Input Source in System Preferences, then double quote ıs on Control i as you mentıoned.  (Using Control for special characters is very unusual on a Mac, normally it would only be Option and Option plus Shift).

If you want to change that, it is quite easy to make a custom layout using Ukelele.  I can help if you are having problems with it.