Allegedly (adverb) = claimed or stated to be so or true. "He was allegedly involved in some illegal deals."
Synonym: reputedly: "The property is reputedly owned by a foundation based in Switzerland."
Antonym: definitively: "It was definitively established that the contract had been entered into under duress."
Other forms of the word:
allegation (noun) - a statement claimed to be true. "The plaintiff's allegation is that the defendant failed to deliver the goods in a timely fashion."
allege (verb) - to claim that something is true. "The prosecutor alleged that the CEO had engaged in insider trading."