Rightful

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Old English rihtful ‘upright, righteous’ (see right, -ful). The notion of ‘legitimacy’ dates from Middle English.

wiktionary

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From Middle English rightful, ryghtfull, riȝtful, from Old English *rihtfull (suggested by derivative unrihtfull(“unrightful”)), equivalent to right +‎ -ful.

etymonline

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rightful (adj.)

Old English rihtful "disposed to do right;" see right (adj.1) + -ful. By late 13c. of actions, "in conformity to what is just or right." The sense of "legal, lawful, legitimate" is from early 14c. Related: Rightfully; rightfulness.