I was granted refugee status in September 2011, and got my green card in March 2012. So I am confused by when should I have to apply for the US Citizenship. I heard regarding my case, 1. I can apply after 4 years. So 4 years from my refugee approval (2011+4) or from the green card (2012+4)? 2. I heard I can even apply 3 to 6 months early is true?

Please advise. Thanks a lot

Do you want to know when you have to apply for citizenship, or when you may apply?

I don't believe you ever have to apply.

"A lawful permanent resident can apply for United States citizenship (https://en.wikipedia.org/wiki/United_States_citizenship), or naturalization (https://en.wikipedia.org/wiki/Naturalization), after five years of residency. This period is shortened to three years if married to a U.S. citizen. Lawful Permanent Residents may submit their applications for naturalization as early as 90 days before meeting the residency requirement.. . (emphasis added)"
https://en.wikipedia.org/wiki/Permanent_residence_(United_States)

So, it appears, you may apply approximately in September of 2015 (or before now if you are married to a US Citizen), and can actually be naturalized about nine months later (or possibly earlier, if you are a spouse of a citizen).