'not never' is a double negative which cancel each other out and is very bad English. It means that the word 'never' cannot be applied in this conext. 'not ever' = never 

thank you mr Leigh,i will remember that.

Eliza

In English you can't say 'not ever' or 'not never'

You could say 'ever' or 'never'.

EVER:

Usually means 'at any time'.  For example:  Have you ever been to London?

Can mean 'at all times'.  For example: Earthquakes are an ever present risk in Japan.

Can be used with 'since'.  For example:  He has been working hard ever since he got the promotion.

NEVER:

Means 'not ever', 'at no time'.  For example: I have never been to Australia.

Hope that helps, Eliza!

thank you for let me know :)

Я не знаю английского. И мне будет трудно спорить с Leigh. Но, я не пойму, почему он пишет, что в английском не используется "not ever". А как тогда понимать это:

Baby can you listen to me? 

I wrote this to you 

This time I'll be true 

You know I can't live without you here 

She's not in my world, not ever again 

Will I be the one that's not your friend 

https://www.youtube.com/watch?v=jaQ8HyA33O0