"Newton" is a very frequently occurring place name in Scotland. In this case it was probably a small village, fermtoun or the like (equivalent roughly to an Irish township).
The session clerk wouldn't have written the entry like this otherwise.
Newton, in Terregles Parish is at the east end of the parish, just over the county boundary from Dumfries. See http://www.nls.uk/digitallibrary/map/early/os_scotland_2nd_ed_list.html and select Sheet 9 - Maxwelltown. Terregles is the small orange coloured parish near the south-east corner of the map. Zoom in on the east end of that parish and you will find Newton.