I don't think may people use travellers cheques these days, they are becoming a thing of the past. I cannot think of anyone I know that uses them. I remember my daughter and I taking them to New York years ago and we struggled to find a Bank that would change them.
Most people bring Sterling with them and then change it in Turkey at a good rate. If you have a Nationwide Account you can draw out Sterling free of charge.. but only Sterling they will make a charge for any other currency, you can then change the Sterling into Lira.
I am sure you may be able to change Traveller Cheques, but perhaps you will need to use a Bank in Fethiye. :