I have skimmed many websites and dictionaries but I really can't understand what it actually means and How and When to use the above word.
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Like the word "allegedly," which is used by news media all the time in the U. S., where there is a legal presumption of innocence of the perpetrator until his or her crime has been adjudicated in a court of law, "supposedly" calls into question the veracity of the statement being made. For instance, if an uneducated person believed that the world is flat and just recently heard that it is a sphere, he might say,
"Supposedly the world is round."
to express his doubts about this newly learned information.
If someone close betrayed you, for instance, you might say,
"I was hurt because she was supposedly my friend."
From the Cambridge dictionary:
supposedly adverb US /səˈpoʊ·zɪd·li/: according to what someone told you, or according to what is believed by many people to be true: The tickets are supposedly in the mail. I’ve been down to the south of England where supposedly King Arthur’s castle was.
More formal than "supposedly," consider the word "purportedly," as you asked in your comment. From Cambridge:
purportedly adverb UK /pəˈpɔː.tɪd.li/ US /pɝːˈpɔːr.t̬ɪd.li/: in a way that is stated to be true, although this may not be the case: The study purportedly found that men married to smart women live longer.
Following on the use of "allegedly" above, my example would be,
"The criminal purportedly was visiting his relatives in another city when the crime occurred."
This use casts doubt on the truth of the perpetrator's alibi for the crime. In general, "purportedly" is both stronger (more judgmental) as well as more formal than "supposedly."
I might say, for instance,
"I'm supposedly losing my hair."
by which I somewhat humorously mean that while my hair is thinning on top as I get older, I still have some hair left on my head.
However, if I were writing a legal document or news report for publication, I might say,
"The defendant purportedly claims he did not know he was breaking the contract when he purchased these supplies from another vendor."
In this sentence I'm using "purportedly" to add emphasis to the doubt I have about the defendant's claim of ignorance.
"Supposedly" is less formal and more common in everyday speech. "Allegedly" is more formal and often used in matters of law and news reporting. "Purportedly" is less common than either and, more importantly, implies a subtle disdain for the person or source making the claim.