"and/not" vs. "and/or"

There are related questions, such as: When should we use "and" and/or "and/or"?

And/or is pretty standard (although some people object to it) shorthand for "either both, or one or the other". For example:

There will be coffee and/or tea

Means that there will be either coffee or tea, or both coffee and tea.

However, I don't understand what you think "and/not" means. Perhaps you need to give a complete example sentence. (And explain what it means.)

But if someone said:

There will be coffee and not tea

I would assume it was an error for "there will be coffee but not tea". (Or maybe coffee and a beverage called "Not Tea" - a hot drink that is almost, but not quite, completely unlike tea.)

In your example of "The first person comes with or without the second person" then you just mean that "Person A will come" and there is no need to mention Person B.