I think that Hugh’s townland on the marriage certificate is Cornahowl (more commonly Cornahawla). That’s immediately adjacent to Cornagee (to the south). He was a servant so if he came from Cornagee he had presumably got work on a nearby farm.
Note that the date of marriage, as shown on the certificate, was 19th November 1878.
The bride’s townland is Mulladeen (more commonly Mullaghdun). That’s immediately to the north of Cornagree. So Hugh married the girl next door.
Mullaghdun parish church is easily found on a modern map. It’s on the Gardrum Rd, near Creenahoe.
Cleenish RC parish baptism records cover 1835-39 and then 1859 onwards. Marriages don’t start till 1866. So if Bridget was born before 1859 (as seems likely) there’s probably no baptism record to find.
Marriage here between James McBarron of Cornagee (son of Pat) to Mary Nolan. So she’s probably the Mary McBarron who was the informant for Pat’s death.
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1879/11066/8048669.pdf
Their 3 children were:
Philip 1.2.1882
Catherine 3.11.1883
Mary 26.8.1885
There was a widowed Mary McBarron in Cornagee in 1911:
https://www.census.nationalarchives.ie/pages/1911/Fermanagh/Gortahurk/Cornagee/517841/
Here’s the birth of her son Phillip:
https://www.irishgenealogy.ie/files/civil/birth_returns/births_1882/02794/2025379.pdf
Possible death for Mary McBarron regd Enniskillen 18th Sept 1923. Aged 73.
There was still at least 1 McBarron living in Cornagee in 1964:
Probate abstract: McBarron, Margaret of Cornagee Letterbreen county Fermanagh widow died 6 March 1964 Administration Londonderry 2 October to Laurence McBarron farmer. Effects £302 1s.
Margaret was 74 when she died so born c 1890. She looks to have been Philip’s widow. They married in 1916.
https://www.irishgenealogy.ie/files/civil/marriage_returns/marriages_1916/09778/5549137.pdf
They had at least 5 children:
James 9th April 1917
Mary 10th Dec 1918
Laurence 27th Sept 1920
Thomas 2nd July 1922
Bridget 3rd Sept 1924.
There may have been later children but the records for those within the past 100 years are not on-line.