Fitton was the eldest son of William Fitton of Awrice, County Limerick and his wife Eva Trevor, daughter of Sir Edward Trevor of Denbighshire.
The will was disputed and lengthy legal proceedings followed involving Alexander Fitton, Lord Chancellor of Ireland (son of William) and Charles Gerard, Baron Gerard, son of Penelope Fitton eldest daughter of the first Baronet.
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Baron Fitton of Gawsworth was a Jacobite peerage created by James II in 1689 for his Lord Chancellor of Ireland, Alexander Fitton ( died 1698 ).