Rightfully

(adv.) According to right or justice.

Thesaurus Entries

appropriately, as is proper, as is right, by right, by rights, condignly, correctly, deservedly, disinterestedly, dispassionately, duly, equally, equitably, evenly, fair, fairly, fittingly, impartially, impersonally, in all conscience, in reason, inequity, injustice, justifiably, justifiedly, justly, meetly, properly, right, rightly, upon even terms, warrantably, warrantedly, without distinction