Very little to go on so I haven't had much luck in the past (30 years) tracing this family and don't have a location to start searching for parish records.
George CLIFFORD (born in Ireland, died before 1880) married (bef.1856 Ireland) Catherine Horkin (born Jan./June 1830/1831, died 12 June 1900 Greenwich, Fairfield, Conn.). According to some records she came to America 1880 and the 1900 U.S. Census says she had 6 children (5 living)- I only know of 4 of the children. The family were supposed to have gone from Ireland to England, George died in England and then Catherine & some of the children went to America but that might not be correct.
1. William Clifford "stayed in England but supposed to have joined the Navy and jumped ship in Australia"
2. Michael Clifford (15 Oct.1856 Ireland-1916 Iowa) married & had family (have their details)
3. George Clifford (18 Mar.1864? or Jan./June 1857? Ireland-1930 Connecticut) married & had family (have their details)
4. Mary Clifford "went to England as a child but moved back to Ireland" however she might be Mary (Clifford) Acker (c1865 Ireland-1930 Greenwich, Conn.). note: unlikely in view of 1850 baptism now found
There are several online family trees that I've come across that are incomplete and full of errors so no clues there. There's a story handed down through young George's family that the Clifford children, and parents, were born in Cork but this might be confused with George's wife whose parents came from Co Cork.