#1 refers to the morning newspaper, as opposed to the evening newspaper, that appeared yesterday. Was it published yesterday morning?
Yes. Daily newspapers generally appear on the day of their publication.
#2 refers to the newspaper that appeared yesterday morning.
I don't understand what you mean here. Was it published yesterday morning or a person got a hold of it yesterday morning but it had been published before?
It was published yesterday morning.
There is little significant difference between the two sentences, exept that the first implies more strongly that there may be afternoon/evening newspapers.