The thing is that not all fonts support European characters (I am from Europe too) and some of the fonts are not supported properly by your mobile device (by some other it might be supported) the best option if you are building website in Turkish is to use default fonts because they are supported on all devices, all browsers and every language there is.
Currently there is no option to change fonts separately for mobile and desktop, so you will have to come up with your own solution for that but I would stick with default fonts or something more common such as Arial, Helvetica that can handle all languages.