There are a few interesting entries in Tongland, the parish south of Balmaghie:
11 July 1800 David Campbell. Father - Anthony Campbell
26 June 1802 William Campbell. Father - Anthony Campbell
This Anthony might well be the one who married Isobell Mcconnel in Twynholm (just to the west of Tongland) 5th Sept 1799.
Then we have your Robert born 5 June 1811 in Balmaghie to Antony Campbell and Mary Shaw and,previously, John in 1809, Balmaghie (see full list at the beginning of this thread)
Ant(h)ony wasn't a common Scottish first name, so this has set me wondering. A second, maybe older Anthony, could be checked for.
I've looked for earlier Campbell births in Tongland and have found an interesting family (all Cambpel) which is also mentioned in the Tongland MIs:
27 December 1771 (b. 26) Penelope - Father - William
16 May 1773 William - Father - William, Mother - Agnas Campbel
15 Feb 1776 Philadelphia (same parents as above)
26 June 1778 Agnas (same parents as above)
9 April 1781 (b. 6) William (same parents as above)
The Tongland MIs have an entry for:
Wm Campbell, esq of Queenshill. Died 27 April 1798 in his 71st year. Daughter Margaret died 12 Sept 1790 in her 27th year. Three infant children - David, William and Philadelphia.
Notes in the MI entry also refers to the Fasti Ecclesiae (a document/book containing information about Church of Scotland Ministers) - William Campbell was a Doctor of Medicine, at one time in Antigua and son of William, one time minister of Kirkinner and grandson of Robert, minister of Stoneykirk.
There is more. I'm not sure whether your Ant(h)ony is related or not but it is worth checking this family out.
Gadget