Gdx.file.internal is read-only. You can use local file or preferences (creates an internal .xml file where you can store small amount of data). It is perfect for game saving.
Take a look at : https://github.com/libgdx/libgdx/wiki/Preferences
You can also use an external file (stored on sdcard), but you can optionally to encrypt it, as it can be edited by the user.