we make a affirmative-negative sentence like "don't ,doesn't, hasn't or do not, does not, has not, have not ,can not,I mean any auxillary+not.

Now question is that, can These "auxillary+not" be seprated by any other part of speech like an adverb or anything else.

Is there any rule for a affirmative-negative sentence for seprating "auxillary"+ "something"+ "not".

All adverbs can assuredly not be placed between auxiliary and 'not', but at least a few can squeeze in there:

I have certainly not eaten your bagel.
They should perhaps not be accepted into the club.
He will undoubtedly not attempt that again.
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The word "not" is an adverb.

I was given a sentence like "I do not know" and was asked to find out the adverb.

I consulted a dictionary and found that "not" is an adverb only.

So, If "not" is an adverb then can I always underline it as an adverb ,If asked.

Apart from an adverb what other part of speech can be placed beween a "auxill." and "not".

I do usually not go to School.

Is above sentence correct?

'Usually' does not work well there, Hanuman. As I said, some do and some don't.

'Not' is always an adverb, as far as I can think; sometimes it's considered a function word, a 'negator'.

I cannot think of another part of speech that can split the auxiliary from its negator, either-- except for nouns and pronouns as subjects in questions, of course: 'do you not like my artistry?'; 'have the elephants not left their enclosure yet?'-- these are quite formal forms.