You didn't say was religion they favored but there is a baptism in Spittal Presbyterian for Alexander Ross born 22 Apr 1803, baptised the 24 Apr son of Lauglin and Mary Ross of Scrammerston Hill in the parish of Ancroft
Also a sibling baptised there: James Ross born 5 Feb 1791, baptised the 8th Feb s/o Lauchlin and Mary Ross of Unthank Square in the parish of Tweedmouth
My guess is this is the one as your Alexander and Jane had a child Lachlane born 3 Oct 1834 and baptised 14 Oct, living Fenton
Wooler Cheviot Street baptisms: Jane Torner born 24 Nov 1799, baptised 28 Nov 1799 d/o James and Rachel Torner of Wooler. This wa a typed transcript so it could be Turner. One place has it indexed as Tarner.
Janis