Hi spacecookie,
If I have the right Census Jasper born c 1862 Eccles, Berwickshire is with DAVID/AGNES Stewart in 1871 down as their Son.
Highly unlikely as they are aged 66/62
1871 Census
Earlston, Berwickshire
David STEWART, 66, Formerly Ag Lab, born Roxburgshire
Agnes Stewart , 62, Wife, born Galashiels, Selkirkshire
Margaret Stewart, 13, Daug, Ag Lab, born Swinton, Berwickshire
Thomas Stewart , 20, Son, Ag Lab, born Makeston, Roxburghshire
John Stewart, 10, Son, Scholar, born Lintad, Roxburgshire
JASPER Stewart, 9, Scholar, born Eccles, Berwickshire
Agnes Stewart, 7, Neice, born Merton, Berwickshire
1861 Census
Linton, Roxburgshire
Dariel STEWARD, 50, Ploughman, born Roxb.
Agnes Steward, 48, Wife, born Linton, Selkirk
Jane Steward, 18, Daug, Ag Lab, born Minto, Roxb.
Alexander Stewart 16, Son, Ag Lab, born Coldstream, Berwickshire
Thomas Stewart, 10, Son, Scholar, born Makerston, Roxb
Charles Stewart 8, Son, Scholar, born Southdean, Roxb
Christina Stewart, 4, Daug, born Linton, Roxb
John Stewart, 1, Son, born Linton, Roxb
1851 Census we have in Roxburghshire;
Daniel Stewart 46, born Cavers, Rox, Ploughman
Agnes Stewart 38
Agnes Stewart 11
HELEN Stewart 10, born Sprouston, Roxb (as described on Anc.)****
Jane Stewart 8
Alexander Stewart 6
James Stewart 4
Mary Stewart 3
Thomas Stewart 7 Mo
Elizabeth DUFF 18
1841 in Sprouston, Roxburgshire we have;
Daniel STEWART, 25
Agness, 25
Agness, 1
HELEN, 4mths***
Trish

EDIT;
Agness STEWART Christened 17 March 1840, Gateshaw Associate Session, Morebattle, Roxburgh, Scotland
Parents, Daniel STEWART and Agness MIDDLEMOST
JOHN Stewart, 27 Aug 1859, Linton, Roxburgh to same Parents except Agness is Middlemist
+ CHRISTIAN, same details, 30 April 1856
(Familysearch.Org)