Sven,
Yes, the day after i wrote I found the child Jacob Roth died as an infant. Now my thinking reverts to my original concept: Jacob Rös(s) must have been Catholic. This is the only reason to have baptized his son in the Catholic church in Chicago in 1856. Therefore, I my current research returns to find his Catholic baptism record in Baden. It will be a several months search to look at 400+ churches’ records where I have previously looked for a marriage record.
Thanks for all your attention and direction.
Best wishes,
Barbara