A. She gave an apple to every of the children.
B. She gave an apple to each of the children.
Would you please show me which one is correct? or if they both could be considered correct?
The word "every" is a determiner, whereas the word "each" is both a determiner and a pronoun.
So, when these words are used as a determiner, you can say:
She gave an apple to every child.
She gave an apple to each child.
As you can use "each" as a pronoun, you can say:
She gave an apple to each of the children.
On the other hand, every isn't a pronoun, so you cannot say "......every of the children".
B is the correct one. 'Every' is a determiner that needs a singular noun with no preposition, here: "every child".