Is the sentence 'Remember the day you saw me' correct?

Let’s look at the sentence :

Remember the day you saw me?

Does the sentence make complete sense?
I think we should add ‘in’ at end of the sentence because we are talking about a time.
I think that should be:

Remember the day you saw me in?

I thought of this thinking:

Remember the day in which you saw me?

So we omit the relative pronoun and place the preposition at the end of the sentence.

Is my concept correct? Please let me know with an explanation.