Northern Ireland births: where the records are
Northern Ireland (Antrim, Armagh, Down, Fermanagh, Derry/Londonderry and Tyrone) became separate from the rest of Ireland in the early 1920s, so its records are split.
Before the early 1920s
Births from 1864 up to the early 1920s are in the all-island records, so you can search them free on civilrecords.irishgenealogy.ie. They are also on GRONI.
After the early 1920s
Use GRONI (General Register Office for Northern Ireland). Searching is free with an account; viewing images and ordering certificates has a small fee.
Other Northern Ireland sources
PRONI holds church records, wills, valuation records and the Tithe Applotment Books for the six counties.
Does a Northern Ireland birth count? The citizenship rules refer to birth on the island of Ireland, which includes Northern Ireland. Please confirm your own case on ireland.ie.