According to someone's allegation.
"The suspect was allegedly seen at the scene, but no concrete evidence has been found yet."
In plain English: Allegedly means something is claimed to be true by someone but hasn't been proven yet.
"The driver was allegedly speeding when he lost control and crashed into the guardrail."
Allegedly comes from combining the word alleged with the suffix -ly to form an adverb. It entered English as a way to describe something that is claimed or stated without being proven true.