Where all are child themes recorded when they are created in WordPress

9 times out of 10, a white screen on a WordPress based site is a PHP error that is not displaying.
You can refer to this Q&A if you want to turn them on.

PHP errors can be caused by anything from missing files in the WP core (very rare), in themes, child themes, or plugins or just plain PHP errors in the code.

Deleting a parent theme, when the child is active, can also be a cause, since the child might be referring to its files and won’t find them.

I suggest you always keep PHP errors on, while developing or debugging issues like that, it will make your job a million times easier, since it will literally tell you what is wrong and where.

DB errors can also occur, however they are relative rare with WordPress, compared to PHP errors incidence. If there is a problem with your WP site not connecting to the DB, WP will let you know.

Finally, always check your server error_log to make sure you don’t overlook errors that might be trickier to show on pages.