In most of the Japanese I was heard and taught, じゃない (and all its variations) would be pronounced exactly as one would imagine. But in Jojo's, consistently, the characters seem to pronounce it (and its variations) more like じゃーない (elongating the "a" of "ja"). Is this some dialect or something? Off the top of my head, I can't think of anywhere people pronounce it like that except in Jojo's, where they do it consistently.
Examples: https://files.catbox.moe/sl22k5.mp4
From the grammatical perspective, it is hardly anything really. じゃない is a contraction of ではない just like "don't" for "do not". In fact, I was a bit surprised when I first learned that じゃない is taught as the canonical form in the JSL grammar. In this light, じゃあない is a less reduced pronunciation than じゃない, thus sounds more emphatic, that is, more likely to appear when they put more stress on negation than usual.
That being said, consistent use of じゃあない is certainly a peculiar style in present-day language. Japanese speakers also notice well that ～じゃあない is a signature wording of Jojo series (e.g. 1, 2, 3). Generally, dialogues in those works are far more theatrical than the everyday language, which contributes to the picaresque ambiance of the universe.
The example speech you give in the mp4 is imitating bad-boy/yakuza/yanki speech. It’s just for theatrical effect. A different example is when Western speech is dubbed into Japanese on TV they often use very theatrical versions of Japanese to make some point. e.g. if it was a old lady on screen they would use the extreme Japanese grandma voice even if her natural speech was not so unusual. Or if it was someone young getting into a fight then a voice similar to the sample. It is almost as if they are signalling the stereotype of the type of person so even if you couldn’t see the screen you’d know what type of person is speaking. Maybe it derives from the theatrical speech tradition in Kabuki.
