As many people would agree, editing WordPress’ core is not recommended because any updates that are made from the official developer (ex: 4.6 to 4.6.1) will override your changes. Plus, editing the core could potentially break your website or any other theme/plugin if it’s not properly edited.
This is where plugins come in, they are packed functions that acts as an add on to enhance your WordPress site.
However, if you do not want to use a plugin to achieve this functionality. Your best solution is to add your custom code in your child theme’s functions.php file which runs your custom codes on top of WordPress.
Update: per Youssef’s comment below
…what code should I add to
functions.phpto get users to verify their email?
It wouldn’t be a few lines of code to add to your functions.php, I can tell you that much.
This will require some work and research on your end since I can’t write up something like this. The right approach is to try and solve this question yourself with your own function. Then, when you run into an issue you can’t solve, that’s where the WPSE community is here for.
We don’t want our members to ask people to create a solution without attempting it themselves.
To start, I’d look into other plugins or functions that are available tailor the codes for yourself. For example, this plugin: User Activation Email is worth looking into. Just download the .zip file and play around with the source codes.
Otherwise, if you are not comfortable with any of this, your best bet is to utilize a plugin that already exists. As I mentioned in my original answer, editing WordPress’ core is not recommended.