I manage to find a solution from @Tetsujin's comment. Using the keyboard configurator for the WhiteFox keyboard, I created a layer of A, O and '. I then use a fn key together with alt/opt (+ shift for CAPS) to write Æ, Ø and Å.
You can use Text Replacement, built into the system.
The issue with needing to generate a single letter in the middle of a word is that the replacer generally wants you to hit a space or a period then a space before it will do the replacement. You also need the trigger to be something you wouldn't ordinarily type.
See System Prefs > Keyboard > Text
The issue is that often conflicts exist between the shortcuts used for changing Input Sources and those used for showing the Spotlight search field.
To check/change these, follow these steps:
Go to Apple > System Preferences
Select the Keyboard preference pane
Select the Shortcuts tab
In the list at left, if you notice a warning icon next to either or both ...
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 ...