Dickson

Statutory registration of births deaths and RC marriages started in Ireland in 1864. Prior to that you need to rely on church records to trace a family. You haven’t said what denomination your families were but if Church of Ireland then Seagoe has records from 1672 (with some gaps). The Presbyterian church (Portadown 1st) has records from 1839 and the RC from 1836.

So the only denomination with baptisms for around 1812 is the Church of Ireland. There’s a copy of those records in PRONI (the public record office) in Belfast. You may be able to find the family there and trace forward.

There are no less than 38 trees on Ancestry witht his family shown. (James is shown as dying in Seagoe in 1874). The couple had at least 1 child Moses Dickson 1841 -1904. He died in Australia.

I’d suggest you contact some or all of the trees on Ancestry to see if they know of any living descendants.