Justly

(a.) In a just manner; in conformity to law, justice, or propriety; by right; honestly; fairly; accurately.

Thesaurus Entries

correctly, decently, decorously, deservedly, disinterestedly, dispassionately, duly, equally, equitably, evenly, fair, fairly, fitly, fittingly, impartially, impersonally, justifiably, justifiedly, meetly, nicely, properly, rightfully, rightly, upon even terms, warrantably, warrantedly, without distinction