I hope this may be of some help to you.My maternal great grandmother was Mary Elizabeth Reggener ("Regenauer" americanized).She originally was from Kent County, DE and I believed later moved to NJ. She married a Samuel King. Lucy Ray King was one of their children and my grandmother.
I have found other information online regarding the name "Regenauer" on ancestry.com.However, nothing regarding an Adam or Frederick.
I would like to hear back from you.Perhaps, we can assist one another.