This I-L38 – FigUre tree is also available as PDF for download: I-L38 – FigUre tree.pdf
When it comes to verifying paternal relationships over several generations, the Y-DNA test is the right choice. My own concern is to verify a family legend that says that my fatherly ancestor came from a certain area of Greece about three hundred years ago. Here you can’t get any further with atDNA. The selection of tests for Y-DNA is extensive. Depending on the motivation for such a test, there are different approaches.