Thanks for your reply. Just to make sure, I went back to the family bible, which lists Jacob's birthplace in his own handwriting. Sure enough, he spells his birthplace "RöthenBERG." So I think you may be right. Since Aichhalden-Rötenberg fell within the Oberndorf Oberamt during the period he lived there, it seems like the logical place to search for church and other records.

By the way, Jacob belonged to the Reformed Church after coming to Pennsylvania. Would I be looking for "Evangelisch" records from Aichhalden-Rötenberg in the LDS library catalog? Or are those Lutheran?