[verb (plain)] + こととて [verb ない-form] + こととて [i-adj] + こととて [na-adj] + な + こととて [noun] + の + こととて
こととて means "since", "as it was": it gives a reason, nearly always as an excuse for a shortcoming or as grounds for asking to be forgiven. It follows a verb or an い-adjective in the plain form, a な-adjective with な, and a noun with の. It is literary, and you meet it in formal letters, apologies and speeches, not in conversation.
The second half is usually an apology or a plea: おゆるし許しください, ごようしゃ容赦ください, おわびお詫びもうしあげます申し上げます. A negative often takes the old form ぬ: しら知らぬこととて.
ので and から are the everyday ways to give a reason, and they work for any reason at all. こととて only fits a reason that excuses something: inexperience, not knowing, short notice.
Without こと, とて after a noun means "even": こども子供とて, "even a child". That is a different pattern.