I (a native speaker from the Western U.S.) would say:

There is no such thing
There is no such thing as a unicorn
There is no such thing as unicorns
There are no such things as unicorns

and *maybe*

There is not such a thing as a unicorn

but that feels pretty old-fashioned, somehow.

I would NOT say:

* There is no such a thing
* There is no such a thing as a unicorn

Do you have links to the places where people wrote "no such a thing"? Maybe I'm forgetting some case, but I don't think I ever say or write that. Perhaps the writers originally wrote "no such thing", then changed it to "not such a thing" while editing, but only added the "a", forgetting to change "no" to "not".