The elder Gleeson earned the nod for his work in "Calvary," while his offspring was nominated for his performance in "About Time." The actors previously co-starred in "Harry Potter and the Deathly Hallows" and "Six Shooter."
Up for the Best Picture IFTA are "Byzantium," "Calvary," "Run & Jump," "The Sea" and "The Stag."
Four of the five best film nominees also get mentions for Best Script -- John Banville for "The Sea," Ailbhe Keogan for "Run & Jump," John Michael McDonagh for "Calvary," and the duo of John Butler and Peter McDonald for "The Stag."
Ruiri Robinson is nominated for Film Director for "The Last Days on Mars" alongside John Butler for "The Stag," Neil Jordan for "Byzantium" and John Michael McDonagh for "Calvary."
Shortlisted for Best Actor along with the Gleesons are Ciaran Hinds for "The Sea" and Andrew Scott for "The Stag."
The nominees for Best Actress are Antonia Campbell-Hughes for "3096 Days," Saoirse Ronan for "Byzantium," Jane McGrath for "Black Ice" and Kelly Thornton for "Life's a Breeze."
Vying for the Best TV Series honor are "The Fall," "Game of Thrones," "Vikings," "Quirke" and "Love/Hate."
Nominated for Best Actress in a TV series are Deirdre O'Kane for "Moone Boy," Eva Birthistle for "Amber," and Mary Murray and Charlie Murphy, both for "Love/Hate."
In the running for Best International Film are "12 Years a Slave," "Gravity," "Philomena" and "The Wolf of Wall Street."
Winners will be announced April 5 at the DoubleTree at Hilton Burlington Road and broadcast primetime on RTE ONE.
"This year's nominations showcase to the world what Ireland's small but excellent film and television community has to offer," Academy Chief Executive Officer Aine Moriarty said in a statement. "Their hard work over the last 12 months has delivered world-class standards with some of the most diverse and engaging Irish films, dramas and documentaries along with great entertainment and factual programs. We look forward to acknowledging and celebrating the great work of the home industry on the ceremony night ahead."