English allows only one negative in an independent clause to express a negative idea; using more than one is an error known as a double negative. Double negatives can be corrected by eliminating one of the two negative words or by replacing one of them with an article or another noun marker such as any.
Negative modifiers such as never, no, and not should not be paired with other negative modifiers or with negative words such as neither, none, no one, nobody, and nothing.
The double negative not . . . nothing is nonstandard.
The modifiers hardly, barely, and scarcely are considered negatives in standard English, so they should not be used with other negatives such as not, no one, and never.