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... Harry had never met a vampire, but he had seen pictures of them in his Defence Against the Dark Arts classes, and Black, with his waxy white skin, looked just like one.

'Scary-lookin' fing, inee?' said Stan, who had been watching Harry read.

'He murdered thirteen people?' said Harry, handing the page back to
Stan, 'with one curse?'

I'm not sure what the sentence means. I searched on the web: fing could be 'thing', 'effing' and etc, but not quite sure what it is in this context. I can't find a reference for 'inee' anywhere.

-- From Harry Potter.

The "standard" spelling is

Scary-looking thing, isn't he?

I'm not entirely sure, but I believe this kind of spelling is called "eye dialect":

Eye dialect is the use of nonstandard spelling for speech to draw attention to pronunciation. The term was coined by George Philip Krapp to refer to the literary technique of using nonstandard spelling that implies a pronunciation of the given word that is actually standard, such as wimmin for women; the spelling indicates that the character's speech overall is dialectal, foreign, or uneducated. This form of nonstandard spelling differs from others in that a difference in spelling does not indicate a difference in pronunciation of a word. That is, it is dialect to the eye rather than to the ear. It suggests that a character "would use a vulgar pronunciation if there were one" and "is at the level of ignorance where one misspells in this fashion, hence mispronounces as well".

The term is less commonly also used to refer to pronunciation spellings, that is, spellings of words that indicate that they are pronounced in a nonstandard way. For example, an author might write dat as an attempt at accurate transcription of a nonstandard pronunciation of that. The rest of this article will discuss the former definition.

(Wikipedia)

There's likely a technical point here I'm unaware of. Anyway, at the very least, the point of this spelling is to show that he speaks very differently from the others. I imagine it possibly reflects a real-world dialect, but I wouldn't know which one.

The English "th" sound is relatively hard to pronounce, and in some English dialects it tends to be replaced by "f" or "v" at the start of words. This is common enough to have a technical name, th-fronting. In the OP's example "thing" is pronounced "fing".

Clusters of consonants tend to be omitted or simplified in some dialects. and "t" in the middle of a word often becomes a glottal stop, so "isn't it" becomes "innit" (which has almost become a word in its own right, used as an indication that someone doesn't speak "correct" English) or even "inni'," with the final "t" turned into a glottal stop. "Isn't he" in the OP's example becomes "inee," or "innee" by analogy with the usual spelling of "innit".

That way of speaking is common in some English dialects like South and East London and northern areas around Manchester. "Fing" is just another way of saying "thing" equivalently "innee" is how some people say "isn't he" in some parts of England. I'd imagine it's to show the character's regional accent.

You're quite right to suggest thing for "fing". "inee" would be a contracted form of "isn't he" therefore the sentence expanded and pronounced would be:

Scary-looking thing, isn't he?

It's common in many dialects throughout England to pronounce 'th' as 'f' and is known as 'th-fronting', so 'thing' could be rendered in writing as 'fing'. It's actually common to the extent that most people don't even realise that they are doing it. The 'inee' bit is referring to 'Isn't he?' but it's obvious that the 'h' is not being pronounced: again, this is quite common.

It's similar to the way that the Spanish language has sounds which are pronounced very differently depending on the country or region of the country to the point where it no longer sounds 'correct' to someone who is learning the language, even though in reality it is normal to just follow the pronunciation which is around you, without worrying whether it is 'correct' or not.