Dental clicks – Wikipedia
Dental clicks may also be used para-linguistically. For example, English speakers use a plain dental click, usually written tsk or tut (and often reduplicated tsk-tsk or tut-tut; these spellings often lead to spelling pronunciations /tɪsk/ or /tʌt/), as an interjection to express commiseration, disapproval, irritation, or to call a small animal. German (ts or tss), Hungarian (cöccögés), Portuguese (tsc), Russian (ts-ts-ts; sound file) Spanish (ts) and French (tut-tut) speakers use the dental click in exactly the same way as English.
The dental click is also used para-linguistically by Middle Eastern languages such as Arabic, Hebrew, Pashto, and Persian where it is transcribed as ‘نچ’/’noch’ and is also used as a negative response to a “yes or no” question (including Dari and Tajiki). It is also used in some languages spoken in regions closer to, or in, Europe, such as Turkish, Albanian, Greek, Bulgarian, Italian, Portuguese, Spanish, Romanian or Serbian to denote a negative response to a “yes or no” question. The dental click is sometimes accompanied by an upward motion of the head.
So Ali, you are onto something: there is one continuum of languages using it for “no”—and another continuum of language in which it conveys disapproval. Spanish and Portuguese, it seems, are common to both.
Turkish is in the middle of the first, and the first is Southern European and Middle Eastern and Central Asian, Spain through to Xinjiang (Wong Yoon Foong’s answer). Turkish could have been one vector of this, but with the feature also turning up in the Western Mediterranean, it can’t be the only vector. Greek or Latin could have been one vector of this, but again, with the feature also turning up in Central Asia, it can’t be the only vector. There’s likelier to have been multiple waves of this feature diffusing.
The feature could be innate and pre-linguistic; but I don’t get the impression that it is: it doesn’t seem to be attested in Africa or the New World.
The feature could be a Nostratic innovation (yes, I went there!), inherited into all of Indo-European, Semitic, and Turkic—diverging in Northern Europe into disapproval rather than negation. But that’s suspect as well, and areal diffusion is likelier.
And paralinguistic features (like grunts) and gestures do diffuse culturally. The head-toss for “no”, mentioned at the end of the Wikipedia quote, is a famous instance of this, turning up in Greece, Bulgaria, and Greek-influenced Southern Italy