Definition from Wiktionary, the free dictionary
supposedly (not comparable)
- As a matter of supposition; in the beliefs or according to the claims of some people.
- People from other planets have supposedly visited Earth in flying saucers.
- According to your testimony, you were supposedly at home watching TV when the murder occurred.
- 2011, Tom Fordyce, Rugby World Cup 2011: England 12-19 France 
- France were supposedly a team in pieces, beaten by Tonga just a week ago and with coach Marc Lievremont publicly berating his players, but so clear-cut was their victory that much of the atmosphere had been sucked from the contest long before the end.
as a matter of supposition