I recently heard:
Try not to blink.
However I knew the following form:
Try to do not blink.
Is one of them wrong? What is the difference ?
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Google Books Ngram viewer indicates that the construction try not to... is about 100 times more common than try to not....
Try to not is a form that has appeared gradually over the past half century.
So you occasionally hear people say things like: Try to not cough so loudly. However, it's certainly more idiomatic to say try not to cough so loudly.
In your second example the insertion of the word do is simply wrong. Omit it.
You will find a similar question about the placing of not at the site below.