The functions in your child theme will be loaded before the functions in the parent theme. This means that if your parent and child themes both have functions called my_function() which do a similar job, the one in the parent theme will load last, meaning it will override the one in the child theme.
~Guide to Functions and Child themes
Further:
Function Priority
If you’re not using your own parent theme, or you’re using a third party one without pluggable functions, you’ll need another method.
When you write functions you can assign them a priority, which tells WordPress when to run them. You do this when adding your function to an action or filter hook. WordPress will then run the functions attached to a given hook in ascending order of priority, so those with higher numbers will run last.
Let’s imagine the function in the parent theme isn’t pluggable, and looks like this:
<?php
function parent_function() {
// Contents for your function here.
}
add_action( 'init', 'parent_function' );
?>
This means the function in your child theme would look like this:
<?php
function child_function() {
// Contents for your function here.
}
add_action( 'init', 'child_function', 15 );
?>
That should get you started…