Hello Eric,
It's lovely to hear that you are tracing a family ancestor!
Before 1864 records were kept in the form of church and parish records so this may be a place to look. The
National Library of Ireland have a website where you can start to look for any records they have. This would be a long process if you do not know which county to start to look in.
There is also the
Irish Genealogy website that has some information on church records and how to search online.
The
John Grenham website on surnames has some information on likely locations for the Quigley surname.
There is an existing post by
Brian Mitchell on
tips to find ancestors which may be helpful, as Derry~Londonderry and County Donegal are popular places for Quigley's, this may be a place to start!
Hopefully, our members and partners may be able to help.