Your objective as a candidate is to have your application advanced to the next stage of the process. The person who reads your cover letter and forwards your application may be influenced by your first sentence, so your words matter.
However, there is no guarantee that the reader will be a native English speaker, so you should write simply, clearly and respectfully, e.g.
I saw your announcement of the PTC Fellowship in the latest issue of th Economist. I am very interested in applying.
It’s okay to be excited or even very excited, but if you’re going to open with that tone, don’t follow it with a heavy, archaic word like hereby. Try something like this instead:
I was excited to hear that the PTC Fellowship in Geneva is open for applications. I have attached the documents that you requested on your website, and I look forward to hearing from you.
It’s not clear who actually reads cover letters these days. A lot of organizations use software tools to manage their applications process. Hiring managers often just glance at screens, sometimes on phones that show only small amounts of text at a time. As an applicant, you need to make every word mean someting.