Alexander's (presumably illegitimate) son, John Alexander Watkins, was born around 1844-46 and his mother's identity is unknown. The following currently is known about John:
He appeared in Aberdeen Post Office Directories from 1867-1868 to 1869-70 as a flesher (i.e.butcher) at 107 George Street and resident at Rose Cottage, Orchard Lane from 1869-70 to 1871-72. Alexander's home was given as Rose Cottage when he died in 1873.
John A Watkins was found in the 1871 census: aged 27, unmarried, a butcher, born Old Machar (c.1844), a lodger at 8 Queen Street Peterhead, with the family of Alexander Sangster, Blacksmith
He died in Christchurch, New Zealand and was buried in the same cemetery as other members of the Watkins family. The death certificate included the following information:
If John's age on his death certificate is correct, he was born c.1846. However, in the Addington Cemetery typescript of monumental inscriptions his age was stated to be 75, giving a birth year of c.1843.
44 years in New Zealand means that he emigrated in about 1874 (5 years before Jessie and family left Aberdeen for New Zealand), though this could not be confirmed from the New Zealand, Immigration Passenger Lists, 1855-1973 available via www.familysearch.org
Searches for John in the 1851 and 1861 censuses for Scotland and England & Wales were unsuccessful, as were searches for a baptism for John Watkins anywhere in Scotland, and for John, any surname, from 1843 to 1847, in Old Machar OPRs and Aberdeen Catholic Registers.