Samuel Miller’s marriage to Margaret Hall was registered in Armagh City 1865, Volume 1, page 63. You can order a copy of that from GRO Roscommon. http://www.groireland.ie/http://www.groireland.ie/
If you think that Samuel Miller was in the Police Force in Ireland, then you could contact the PSNI museum (police museum) in Belfast, which has copies of the records of all former Royal Irish Constabulary staff. That normally records the county where someone was born. (And sometimes you can narrow that further by researching the career of the Police Inspector who recruited them).
If you think he also served as a police officer in Glasgow, then he probably served with the City of Glasgow force, which nowadays is part of the Strathclyde Police force. You could try their museum to see what records they hold.