Please make sure, you are interested in negating suffixes, right?
Assuming you understand what is a suffix at least in English....
Are -ない、-くない、‐ではない、‐なし、‐ぬ、‐ず、 and ‐まい a kind of suffix?
Among these, only
-なし can be grammatically called a suffix. It can form derivative nouns that mean "someone/something without ～" or "～-less one".
- 名なし: (noun) an anonymous/nameless person
- 一文なし: (noun) a penniless person
- 能なし: (noun) a dumb, a fool (lit. "one without ability")
All others are grammatically classified as something other than suffix. Basically these are more fundamental parts which are more like English "not", "may not", "is not" or such. Of course you don't call these "suffix", do you?
As @choco said, there are several negating prefixes in Japanese. See: 不 and 非 and 無 and 未 usage difference/rule