I read this in a text book:
My test is on 22th of June.
I saw this in a YouTube tutorial:
My test is at 22th of June.
Which sentence uses the right preposition?
A variation of your first sentence:
Although you may write on June 22, 2013, in a conversation I would say on the 22nd of June - notice the the and the nd ending of the 22nd. Alternatively you can say on June 22nd.
More here In, At, On + Time or Date