His mother, Arabella Cathcart, was the daughter of a farmer, and the tenancy, under Lord Conway, of the farm at Derriaghy was her marriage portion.
in July 1728, and, after teaching in the endowed school of Dundalk, was nominated curate to Samuel Madden of Drummilly, County Fermanagh, and ordained deacon by John Stearne, bishop of Clogher, in 1729.
He studied physic and prescribed for the poor, argued successfully with profligates and sectaries, persuaded lunatics out of their delusions, fought and trounced a company of profane travelling tinkers, and chastised a military officer who persisted in swearing.
In 1750 Skelton was given the living of Templecarn, a large parish in the counties of Donegal and Fermanagh, consisting of wild moorland surrounding Lough Derg, in which is St. Patrick's Purgatory, the most famous place of pilgrimage in Ireland.
He published anonymous discourses against Socinians, and in 1736 an attack on Benjamin Hoadly's views of the Eucharist, entitled A Vindication of the Right Rev.
In 1744 Skelton published The Candid Reader, a satire on the verse-making of Hill the mathematician, on the Rhapsody of Lord Shaftesbury, and the Hurlothrumbo of Samuel Johnson.
In the same year he issued A Letter to the Authors of the Divine Analogy and the Minute Philosopher, and in 1745 The Chevalier's Hopes, a paper in which he showed Whig principles.
In 1784 he published An Appeal to Common Sense on the subject of Christianity, thirteen hymns and a Latin poem, and in 1786 Senilia, and a short account of Watson's Catechism.
The retired Dublin printer, Sarah Cotter was so inspired by An Appeal to Common Sense on the subject of Christianity, she offered and paid for a cheaper edition of the book to allow for a wider circulation of the text.
Skelton gave Cotter permission to have a portrait drawn of him on the condition that it not be copied and that she destroy it before her death, which she did three months before she died in March 1792.