How category or taxonomy data on its admin panel get populated?

The category or taxonomy manage panel get populated by get_terms function.

I found that in there is a file call wp-admin\includes\class-wp-terms-list-table.php to populate data in either category or taxonomy table in the manage page

Here is the code excerpt from the file above

function display_rows_or_placeholder() {
		$taxonomy = $this->screen->taxonomy;

		$args = wp_parse_args( $this->callback_args, array(
			'page' => 1,
			'number' => 20,
			'search' => '',
			'hide_empty' => 0
		) );

		extract( $args, EXTR_SKIP );

		$args['offset'] = $offset = ( $page - 1 ) * $number;

		// convert it to table rows
		$count = 0;

		$terms = array();

		if ( is_taxonomy_hierarchical( $taxonomy ) && !isset( $orderby ) ) {
			// We'll need the full set of terms then.
			$args['number'] = $args['offset'] = 0;
		}

		$terms = get_terms( $taxonomy, $args );

		if ( empty( $terms ) ) {
			list( $columns, $hidden ) = $this->get_column_info();
			echo '<tr class="no-items"><td class="colspanchange" colspan="' . $this->get_column_count() . '">';
			$this->no_items();
			echo '</td></tr>';
			return;
		}

		if ( is_taxonomy_hierarchical( $taxonomy ) && !isset( $orderby ) ) {
			if ( !empty( $search ) ) // Ignore children on searches.
				$children = array();
			else
				$children = _get_term_hierarchy( $taxonomy );

			// Some funky recursion to get the job done( Paging & parents mainly ) is contained within, Skip it for non-hierarchical taxonomies for performance sake
			$this->_rows( $taxonomy, $terms, $children, $offset, $number, $count );
		} else {
			$terms = get_terms( $taxonomy, $args );
			foreach ( $terms as $term )
				$this->single_row( $term );
			$count = $number; // Only displaying a single page.
		}
	}

However if you want to filter the taxonomy or category value in its table you don’t need to go into this file

rather you will create a function() and use add_filter(‘get_term_args’, ‘my_filter_function’,10,2)
function my_filter_function($args){

//code goes here
return $args;
}

then add the add_filter and function to your theme’s functions.php

all credit goes to: Mamaduka and his code in the link below
https://wordpress.stackexchange.com/questions/30911/excluding-categories-from-manage-categories-using-a-get-terms-filter