What would happen is entirely your responsibility as the author of the scenario.

Some options may be more “realistic” than others, but since the existence of a working time machine is already beyond what seems to be feasible physics (requiring ridiculous amounts and density of negative energy for example, where not even any has been shown to be possible to make) the scenario becomes soft sci-fi, or in other words magic, and that means it’s up to the writer to make up the rules.

Here is a post I found with many of the options you can choose from.