"thing" is a countable word. (source). But I can frequently find both
no such a thing ...
no such thing as ...
Which one is correct?
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Like those who have commented, I find "no such a thing" to be ungrammatical, and think that the instances you have found are mistakes. However, looking in GloWbE (the corpus of Global Web-based English) I find 133 hits for it, against 12745 for "no such thing" - about 1% - Looking at them I suspect that what is going on is that some people actually say "no such thing", but when writing they are unsure whether the phrase is 'supposed' to be "no such thing" or "no such a thing", and they write the latter. I cannot prove this idea.
But certainly, "no such a thing" is not grammatical in any standard English that I am familiar with.
The reason is that "no", as well as being a quantifier, is also a determiner, like "each", and cannot be accompanied by another determiner.