illegitimate
1 illegal, illicit, improper, unauthorized, unconstitutional, under-the-table, unlawful, unsanctioned
2 baseborn (archaic) bastard, born on the wrong side of the blanket, born out of wedlock, fatherless, misbegotten (literary) natural, spurious (rare)
3 illogical, incorrect, invalid, spurious, unsound
1 authorized, constitutional, lawful, legal, legitimate, proper, sanctioned