"for allegedly" is correct and usable in written English.
It is typically used when referring to something that may be true or false. Example: The police arrested him for allegedly stealing a car.
Are you still getting criticism for allegedly "shaming" thin women?
She is accused of negligence for allegedly approving the flight.
In 2007 she was arrested for allegedly assaulting a paparazzo.
They don't get to kill you for allegedly stealing cigarillos, and they don't get to kill you for allegedly selling loosies.
Prosecutors are investigating a popular television comedian for allegedly insulting the President.
In April, his political secretary was arrested for allegedly rigging bids for public contracts.
HSBC is expected to receive a hefty fine for allegedly flouting money-laundering regulations.
And a Dutch sixteen-year-old has been arrested for allegedly hacking in support of WikiLeaks.
Three judges have been sacked for allegedly viewing porn at work using official judiciary computers.
After Edward ascended the throne, Eleanor was criticized for allegedly mistreating the tenants on her lands.
He is on trial for allegedly taking bribes from a Finnish arms company.
