Jacobus in RC baptism records was usually used for James. Something like Joannis was used for John.
Many Irish back then did not know their birthdate, so that is not always reliable, even when provided by them.
Most Irish of that generation followed traditional Irish naming convention and named their first son for the father’s father.
Many parishes don’t have registers available back to the early 19th century, so a baptism record might not exist.
Have you found his marriage record? They sometimes show parents’ names.