Kote Betta means Fort Hill, but the climb is remembered today for a high ridge, a Shiva shrine and a Western Ghats horizon. A place-name is evidence of memory; it is not a licence to invent surviving battlements.
What the record supports
Karnataka Tourism places the mountain about 15 km from Madikeri, calls it one of Kodagu’s three highest peaks and gives an elevation of 1,620 metres. OpenStreetMap node 4807012652 identifies the named summit at 12.5365245, 75.7575502. Neither source documents a standing fort on top.
How to read the place
Look at the terrain that may have made the name persuasive: an elevated, defensible ridge with long views. Give the small summit shrine its own space, and describe visible walls only after identifying what they actually are.
Keep Kotebetta distinct from nearby attractions. Their photographs, opening hours, permissions and facilities cannot be transferred to this site.