Modifying Core Files?

I would like to make a few small changes to the way some parts of WordPress work on my site.
This ultimately means adding 1 or 2 lines of code to certain files in the wp-includes folder.

The problem that I have is that they’ll most likely be overwritten when I update WordPress.
So, I’d like to know if there’s a way of making child templates for core files like there is for themes?
Or if my only option is to backup my custom files before updating and restore them afterwards?