bo,
There are civil parishes (which is what we use on Ireland Reaching Out) and there are Roman Catholic parishes. Sometimes the RC church uses the civil parishes boundaries but often not. (They tend to prefer larger parishes). And sometimes they give their parishes different names, and sometimes not. All a bit confusing.
The River Bann is the body of water you are referring to and forms the border between Counties Antrim and Derry/Londonderry. A friend who lives on the river bank says that in earlier times it took a different, more circuitous route and that all of Ballyscullion was once a single parish in Co Derry but then the river changed its course or was straightened to improve navigation, and as a consequence part of the parish ended up in Co. Antrim. I am not certain that’s correct because I don’t see any traces of a dried up river around the Antrim parish boundary. Whatever the actual explanation (and no-one here really knows or cares) the bigger civil parish is in Co. Derry and the smaller in Antrim. If your ancestors did come from the Antrim parish that’s helpful because it's smaller but it is still a very common surname, and it’s always hard to sort the various families out. (And the spelling varies all the time eg Scullen, Scullan, Scullon, Scullion and so on).
The RC church uses the modern river as its parish boundary so all of the RC parish of Ballyscullion is in Co. Derry with the bit in Co Antrim being in the RC parish of Duneane.
So if you think the family came from Co. Antrim I would start by looking at the records for Duneane RC parish. They start in 1834 and are on-line free on the National Library site:
https://www.nli.ie/en/family-history-introduction.aspx
The Ballyscullion parish records are on the same site but they only start in 1844 so may not be much help.
Bridget arriving in the US with the children, but without her husband would make you wonder if he had died. However there were no statutory death records in Ireland in the late 1840s and so establishing that may be difficult.
I had a look briefly at the RC baptism records. There was a Bridget Scullion baptised in Duneane on 11.4.1845 but her parents were Owen & Mary Scullion. But is Bridget born 1815 the mother of the 4 children who accompanied her. I don’t suppose you know for certain. Perhaps she was an aunt.
You mention DNA testing. Family Tree DNA reportedly has more people with Ulster roots than any other company. That obviously increases the chances of finding a match. You might want to try them or, if you have already tested, you can transfer your results to them for no fee.
The North of Ireland Family History Society is running an Ulster DNA project in conjunction with Family Tree DNA and can offer testing kits at a reduced price. http://www.nifhs.org (Go to DNA project on the website). You don’t need to be a member of the NIFHS to participate in the DNA project.
