In accordance with what is right or just; fairly.(adverb)
Rightly, correctly.(adverb)
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Use "rightfully" in a sentence
"Today, the title "video artist" could be claimed by any kid with a camera, but the label rightfully belongs to Viola, who harnessed the potential of high-definition technology to produce evocative and startling snippets of video for museums and installations."
"She also said this: the public rightfully is still making it anissue"
"He acknowledged that most Americans remain "rightfully angry" at seeing their government bail out the financial firms whose recklessness sent the housing market into a tailspin, triggered a wave of unemployment and wreaked havoc on the economy."