Pegasus and Turkish will require you to pay for a type rating (which will cost wayyyy more than doing it in the US, since you'll be doing it in a JAA environment).

Turkish requires FAA-certified pilots to have 3000+ hours on glass cockpit aircraft >27,000 tons (which I'm sure you have by now). Go apply via CAE-Parc. I don't think Pegasus hires foreigners unless they're paying for their 500-1000 hours via a line training scheme.

The OP likely went through Pegasus flight academy, and purchased a 737 TR in addition to initial/commercial license training. Not sure if he also paid for 500 hours on type, but that's kind of par for the course in Europe these days (thank God that system doesn't exist here or half the RJ FOs with rich parents would be buying "jobs" at United/Delta/AA as we speak).