Hello Patrick,
Thank you for this research! It is a big help.
The head of the family in the 1901 census record you found is Margret Gott, age 61. I'm assuming that she is a widow and may have been the wife of one of Andrew's brothers. Her son James, age 38, appears to be the couple's oldest child. If his parents followed the traditional Irish naming pattern as I understand it, James would have been named after his father's father who would have been James Gott, possibly the father of Andrew. A great clue to follow up on!
Andrew Gott put a notice in the Boston Pilot in August of 1861 looking for information about his brother William who had emigrated to the United States in 1847 and was last known as living in Canada West. He mentions that William was a native of Deehacher, County Fermanagh. There is of course no townland by that name. Someone suggested that at that time a Bostonian wouldn't have known anything about Northern Ireland and spelled the townland as he heard it orally from Andrew or that if it were written, he couldn't read Andrew's handwriting. They thought perhaps the townland could have been Doohatty Glebe.
Again, many thanks for your assistance.
Pamela