I have been looking at the TEI's website for a few minutes, the one thing that has caught my eye is the level of integration TEI has with major Western Engine giants: Rolls Royce, Safran and especially GE. I wish Indian Private Sector giants like Kalyani could think about this kind of partnership with established engine manufacturers. TEI's manufacturing is top-notch.
However regarding parts that TEI supplies for foreign engines like the LEAP or GEnx, etc: It doesn't seem as though these parts, their materials or their processes were designed by TEI. It appears to be the case that Western Engine Giants provide TEI with the raw material as well as the process and gets them to manufacture certain engine parts. This arrangement is similar to how India's HAL makes AL-31, Turbomecca Shakti and other engines that were primarily designed by foreign manufacturers and their processes for assembly and manufacturing of components was provided by the foreign manufacturers to HAL. If this is the case, then TEI doesn't hold the IPR of these parts, such as the blisks it makes as part of the LEAP engine HPC.
Looking at turbofan engines TEI has developed itself, these appear to be mostly small turbofan engines, smaller than India's Manik Turbofan. The biggest project under development using own technology in TEI (as per their website) seems to be the TS1400 turboshaft engine. This is similar to the Indian HTSE-1200 turboshaft engine being developed by HAL. The fact that Turkey is using a particular kind of single-engine turbine blade and thermal barrier coating on the TS1400 means that that is the particular technology for which they hold IPR.
It appears to me that in TEI is like India's HAL while TUBİTAK-MAM is like India's DRDO-GTRE. So it would be great if you could provide me some links pointing out the work of TUBİTAK-MAM in this area. TEI appears to be more of a manufacturer than an R&D organization. I've visited the website of TUBİTAK-MAM, but can't really find much info. I hope you'll be able to find more on TUBİTAK-MAM's work.