This is a possible way of doing this.
Whenever a new term is created, you execute the following code.
This code saves the current user_id as the term author, which should allow you to filter by user_id when fetching terms.
add_action( 'created_term', 'filter_user_specific_term', 10, 3 );
function filter_user($term_id, $tt_id, $taxonomy){
if( $taxonomy == "my_custom_taxonomy"){
if (isset($term_id)) {
add_term_meta ($term_id, "author", get_current_user_id());
}
}
}
To get the term list, according to current user:
$terms = get_terms( array(
'taxonomy' => 'my_custom_taxonomy',
'meta_key' => 'author',
'meta_value' => get_current_user_id() ) );
I didn’t test this code but should be a good start point for doing what you want.