Claudius was the illegitimate son of William Quayle and Esther Kermod bapt Maughold 19 Feb 1804. George, illegitimate, son of William Quayle & Esther Kermod bapt 10 Jan 1808.
[Maughold parish registers]

There were quite a few William Quayles in Maughold so it is pretty difficult to guess which one - you might have more luck with William's will, because illegitimate children were often mentioned.

If bapt in Maughold he could have been William son of William Quayle and Ann Kennish bapt 28 Mar 1783
or
William son of Samuel Quayle and Alice Curghey bapt 14 Mar 1779

Around the same time that Claudius and George were bapt [early 1800s] there was a William Quayle with wife Ann Corteen having children baptised.

Claudius Quayle married Margaret Fargher in Maughold 16 Sep 1831, and was buried aged 31 on Jun 29 1834.

Wm QUAYLE aged 61 buried Dec. 8 1834

William QUAYLE aged 70 of Bwoalley Velt buried 29 Nov 1849

George QUAYLE aged 72 yrs of Maughold buried May 19 1880

Sue