The phrase "allegedly high" is correct and usable in written English.
It can be used when discussing claims or accusations regarding someone's elevated status, level, or measurement that has not been definitively proven.
Example: "The defendant was allegedly high at the time of the incident, according to witness statements."
Alternatives: "reportedly high" or "supposedly high".
[Daily News] The police arrested a 25-year-old woman wearing a Manning jersey on Long Island on Tuesday, who was allegedly high on drugs.
And Marcus's leaps from so-called low culture to the allegedly high were embodied in sentences at once down-on-the-ground and thrillingly performative.
He didn't bother kids whose fathers were in local politics (my dad was in the State Senate) or allegedly high up in the mob (a couple of Gambino grandsons went to our school).
Mr King was a fearsomely strong man, allegedly high on drugs, who tried to flee from the police in a high-speed car chase and then attacked them when they tried to arrest him (hardly things that justify what happened to him, but all factors that had a great impact on the white jury that initially acquitted the LAPD officers who beat him).
Allegedly high on amphetamines and booze and out to shock, Costello refused to apologise in a press conference for his remarks (his defence at the time was a curt "I'm not a racist", and he had indeed played Rock Against Racism gigs), but he has been contrite on plenty of occasions since, a transgression presumably high up in his list of regrets.
To protest the allegedly high level of taxation in the United States, various right-wing groups are organizing tea parties around the country in the spirit of the Boston Tea Party of 1773.
Standard of questions, dismal for allegedly high-powered assembly, seldom rises above gossip level; e.g.: Q: As a regular viewer, may I ask why you have switched from wearing a Windsor knot to a four-in-hand?
His allegedly high-minded agenda is to protect "American freedoms" by striking back at terrorism directed against the United States with a brutality so fearsome that terrorism will soon cease to exist.
Unfortunately again, the British establishment is a small world, and Ms Woolf was a friend and neighbour of Leon Brittan, home secretary when the Home Office received and lost a dossier on allegedly high-profile abusers raping children.
On the other hand, the increasing extent of A. dealbata (93% said it was increasing) exacerbates local household vulnerability though reported reductions in cultivated areas, crop yields and forage production, and allegedly higher risks of crime.
Armed with Hutchinson's ID, credit cards, and car keys, she allegedly high-tailed it to Texas the last place anyone's spotted the sedan she allegedly stole.
