Those points on a mesh are called “vertices”. When you have just one, it’s a “vertex”. I think some people think from the pronunciation of “vertices” that it’s actually spelled “verticies”, and back-construct a singular from that. To remember the right form, just consider that another common plural form is “vertexes”.
The same thing seems to happen with another word, singular “index”, plural “indices” or “indexes’. Same principle applies, same way to remember the right one.