Family and early career
He was born in Cavan, Ireland, the son of James Sheridan, and grandson of the Reverend Dennis Sheridan. Two of his uncles were William Sheridan, Bishop of Kilmore and Ardagh and Patrick Sheridan, Cloyne, the Bishop of Cloyne. After graduating from Trinity College, Dublin, he married Elizabeth MacFadden and the couple first lived in Dublin in King James's Mint. He inherited from his father-in-law a substantial property at Quilca in County Cavan. He ran a school in Capel Street, Dublin in the 1720s, whose pupils included children of many prominent families such as Anthony Foster, the future Chief Baron of the Irish Exchequer, and Philip Tisdall, the future Attorney General for Ireland.
He was the father of Thomas Sheridan, a celebrated actor and elocutionist, who was in his turn the father of the celebrated playwright Richard Brinsley Sheridan; he had two other sons and one daughter.
In 1725 he was appointed a royal chaplain, but preached a sermon which was considered by some to be politically suspect, and his appointment was cancelled. In compensation he was given a living at Drumlane in Cavan and in 1735 became headmaster of the Cavan Royal School where he remained for three years. Other appointments he is reputed to have applied for were the position of Dean of Kilmore and the position of headmaster of the Royal School in Armagh, but neither was successful.
Friendship with Swift
He was friends with Jonathan Swift, and had a room permanently reserved for him in the Deanery; he was his principal collaborator and wrote his biography. Swift often stayed at Sheridan's country house and wrote part of Gulliver's Travels there On the much debated question of whether Swift was secretly married to Esther Johnson ("Stella"), Sheridan was a strong if not conclusive witness that the marriage did take place; according to friends his source was Stella herself.
Like so many of Swift's friends, he was ultimately fated to quarrel with him irrevocably: in 1738 Swift told him that he was no longer welcome at the Deanery. Apart from Swift's increasing eccentricity, the cause of the quarrel is obscure: by one account Sheridan rebuked Swift for his growing avarice, which Swift thought unforgivable.
Death and reputation
Swift before their final quarrel called him the best scholar in Ireland; Sir Walter Scott in his Life of Swift calls him "good- natured and light- hearted."