Not so fast - who says you become a "replica" in the first place? Assuming time travel replicates things, then yes, what you said holds true.
But as I understand it you don't replicate, your time just loops back on itself. So looping back to a time before you were born and killing your father would create a paradox.
You seem to have not understood what I said. I did not say time travel would replicate anything.
You would simply be transferred to the past, without any connection to the outcome of that past.
I.e. Let's say that you are transferred back in the 50s and you go kill your father before you were born. Then nothing will happen, there would be no paradox, you will continue to exist in that universe.
But as I understand it you don't replicate, your time just loops back on itself. So looping back to a time before you were born and killing your father would create a paradox.