Robert Selfridge

A high percentage of migrants from Ireland in the 1700s were Presbyterian (so Scots-Irish, or Ulster Scots as we know them).  90 Selfridges in Ireland in the 1901 census. All Protestant, mostly Presbyterian or Church of Ireland, so that indicates they were incomers, and that many came from Scotland (in the 1600s).

Statutory birth, death and marriage registration (in some jurisdictions called Vital Records) only started in Ireland in 1864, save for non RC marriages which were recorded from 1845 onwards. So you won’t find statutory birth, death or marriage certificates in Ireland for this family. For earlier years you usually need to rely on church records, where they exist.  Ideally you need to know the precise denomination and have some idea of where the person was born in order to search the correct records. Otherwise it’s a needle in a haystack. Not all churches have records for that period and not all that do are on-line.

RC records are mostly on-line on the nli site:  

https://www.nli.ie/en/family-history-introduction.aspx

For other denominations, in Ulster, the churches usually hold the originals but there are also copies in PRONI, the public record office, in Belfast. A personal visit is required to access them. Access to the records there is free. This link explains what records exist, parish by parish:

https://www.nidirect.gov.uk/publications/proni-guide-church-records

If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net

Bear in mind that the 1766 census is not complete. A lot of it was lost, so there may have been other Selfridge households not listed in the current on-line data. And only heads of household were named so if your ancestor (who was about 15 in 1766) was living with his parents or lodging somewhere, he wouldn’t be listed anyway.

Researching in Ireland in the 1700s is very hard going due to the general lack of records. If you don’t know where they lived it’s a needle in a haystack. Ideally you need to know the person’s exact denomination and the townland or parish they lived in to have any chance of finding them, and even then there may not be any records for that location.

Possibly DNA testing may be a way of matching with others who have additional information about where the family originate. 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 FTDNA and can offer testing kits at a reduced price.  http://www.nifhs.org (Go to DNA project on the website).