The Penal laws introduced in the late 1600's limited Catholics rights to land, they also forbid Catholics to teach school. This forced the creation of hedge schools where Catholic children were taught in secret by teachers who travelled the country and were paid by the parents of the children they taught. With Catholic emancipation in 1831 a new education system was introduced that was finally gave Catholics a route to formal education. As it established a national primary school system.

There were a relatively large number of schools at the time. There are records available in the National Archives that can provide some valuable information.

The Book, 'A Topographical Dictionary of Ireland' gives information about the schools existing in Ireland in the  mid 1800's.

The National Archive holds a number of records; Registers, Daily Report Books and Roll Books.

Probably most valuable are the Registers. They list all pupils attending a given school; but can also list date of birth, religion, and parent or guardian.

Daily Report Books records the day to day attendance of pupils. And Roll Books give a higher level records of the name and number of pupils in a given class.

The archives hold records from the early 1800's right through to the 1900's. It is possible to find the records available for any given county

There are other records available, so you should contact the National Archives if you intend to carry out further research

There were over 3000 schools in Ulster in 1821, but only in 1831 was an Irish System of National Education founded giving some structure. For more information on Ulster Records, http://proni.nics.gov.uk/records/school.htm