Looking at the map which accompanies Griffiths Valuation, you'll see that Ballycastle townland is immediately north of Ballycastle Town.
www.askaboutireland.ie/griffith-valuation
Select "Griffiths Places" and search for Ballycastle in Mayo. 3 results, all in Doonfeeny civil parish, Tirawley barony . No Ward holdings in any of them. There were several vacant holdings. Griffiths Valuation was published around the time of Thomas Ward's birth. Select a map view. Click "Show towns" to get exact location of Ballycastle. Then click "Show name books" to locate Ballycastle townland. Enlarge map to see it in detail. Click on icon for Ballycastle townland to access data sheet for it.
This is from the data on Ballycastle townland: "Part of the Townland is held as Town Parks by the inhabitants of Ballycastle Town, part of which stands in Townland. The rear is let to tenants by leases of 1 life at £2 per acre."
SWilson.Info is useful for identifying places, parishes, registration districts &c. https://www.swilson.info
Ballycastle is in Killala Registration District for births, marriages and deaths.
Do you know Thomas Ward's religious denomination? R.C. parish is Doonfeeny & Ballycastle in Killala diocese. Filmed parish registers on National Library of Ireland website start 1864. Too late for baptism of Thomas but if he had younger siblings they may have been baptised there. https://registers.nli.ie/parishes/0739