What does Basilidiānus mean in Latin?

Basilidiānus, a noun, means “Basilidian”.

What is the genitive of Basilidiānus?

The genitive singular is Basilidiānī. Basilidiānus is masculine, second declension.

noun · masculinesecond declension

Basilidiānus m sg (genitive Basilidiānī)

Borrowed from Byzantine Greek Βασιλειδῐᾱνός (Basileidĭānós). By surface analysis, Basilidēs + -iānus.

Descendants

adjectivefirst/second-declension adjective

Basilidiānus²

Basilidiānus (feminine Basilidiāna, neuter Basilidiānum)

adjectiveBasilidian
[...] & nullos propterea ſecta Baſilidiana martyres habebat, nec qui ei dediti erant, gloriam martyrii affectabant.1753, De rebus Christianorum ante Constantinum Magnum commentarii, page 360:

singular
form	masculine	feminine	neuter
nominative	Basilidiānus	Basilidiāna	Basilidiānum
genitive	Basilidiānī	Basilidiānae	Basilidiānī
dative	Basilidiānō	Basilidiānae	Basilidiānō
accusative	Basilidiānum	Basilidiānam	Basilidiānum
ablative	Basilidiānō	Basilidiānā	Basilidiānō
vocative	Basilidiāne	Basilidiāna	Basilidiānum

plural
form	masculine	feminine	neuter
nominative	Basilidiānī	Basilidiānae	Basilidiāna
genitive	Basilidiānōrum	Basilidiānārum	Basilidiānōrum
dative	Basilidiānīs	Basilidiānīs	Basilidiānīs
accusative	Basilidiānōs	Basilidiānās	Basilidiāna
ablative	Basilidiānīs	Basilidiānīs	Basilidiānīs
vocative	Basilidiānī	Basilidiānae	Basilidiāna

Borrowed from Byzantine Greek Βασιλειδῐᾱνός (Basileidĭānós). By surface analysis, Basilidēs + -iānus.