Ok this is a very broad quetion and quite complex. As far as I know my entire family history is Ashkenazi Jews. I just took a DNA test to confirm this.
My Mom side tested for the K haplogroup. A new research report believes this originated in Northern Italy about 2000 plus years ago when Italians pagans converted to Judaism.
My Fathers side on the Y tested for the SNP L47 mutation which is popular in Germany. Also big in GB and Ireland due to Saxon invaders. However, I know of zero history of any German Pagans converting to Judaism. The Jewish groups that moved into the Rhine were very isolated and tiny communities in the early Middle ages.
Any clues to the German connection.