Synonyms for purportedly

The 100 block is still paved with cobblestones "big as beer kegs" purportedly laid by Hessian prisoners during the Revolution.

And do you understand that it was purportedly something that Lee Harvey Oswald claimed to have made up himself?

Well, photographs that he had purportedly taken, or picture postcards or things he had purchased?

That purportedly quoted me about not wanting the President to ride in a motorcade or caravan in Dallas.