אילן הש"ך

I can offer one way of pursuing your research. Do the genetic test called ydna haplogroup and see if you match other descendants of Rabbi Shakh. Then you can work together to build the tree.

האם יש אולי עוד דרך?

Yes there is always the search for documents, but for this you may need a genealogist with expertise in European records, probably located in Europe as well.

Avraham Blumenfeld are you a Cohen?

Avraham Blumenfeld
In order to be a descendant of
HaRav Shabty Ashkenazi HaCohen Katz, the "SHaCH"

Son after son, you must be from the choanim family (through your father and his father).

I checked the relationship that now exists between you and him, and you are his cousin (5), through your mother, and her mother, and on the way to him there are other ancient mothers.

even if you are son after son a descendant to him , you are missing many generations down to him.
The only option I see is to perform agenetic test. .

גם אני בן אחר בן, ואשמח לעזור לך כדי למצוא מידע על הדורות בינו ובינך. פשוט שלח לי הודעה ישירה.

אני כהן
Avraham Blumenfeld