I just discovered a link to a Bernhart Adam (d.1809 or 1810 in Cumru,Berks County PA). Here is his will:
ADAM, BERNHART, Cumru.
April 4, 1809 - September 10, 1810.
To 2 daus. Juliana and Margaret my lands in Cumru, tract know as the church land containing about 4 acres during their lives.
All other property to be sold and divided among 9 children, viz: John, Nicholas, Barnet, and daus. Juliana, Anna Maria wife of John GARBER, Margaret, Leah wife of John REESER, Rachel late wife of John SWARTZ deceased, and Salome wife of David MEYER.
To Dinah, the illegitimate dau. of said dau. Salome £100.
Exrs: Sons John, Nicholas and Barnet.
Wits: Henry WOLF and Joseph BRIGHT.
Could this be the son of your Anthony Adam? Look forward to hearing from you.