Hi John,
I don't have a record of Peter's birth but, if you are sure he was born in Creggan in 1860, he is almost certainly a son of James O'Hagan b. 1825 and Rose Quinn who lived in Cornonagh townland, Creggan, Co. Armagh. They were married in 1859 and had 5 children (ref. 1901 census). Other children were Lawerence b. 1862 (went to Durham, England), James b. 1864, Mary b. 1867 and Richard b. 1875. If you search the irish census 1901/1911, see
www.census.nationalarchives.ie/ you will find James/Rose and James Jnr & Richard living in the this area.
If you send me an email address I can provide a fair bit of information on this family. Note that your Peter O'Hagan and the Peter O'Hagan this thread is about (Al Bye's grandfather)were first cousins.
Hope this is helpful,
Regards,
Ken.