Add a Color Control field to the WordPress Customizer.

WP Customizer - Color Control

$wp_customize->add_setting( 'core_color_setting_id', array(
  'sanitize_callback' => 'themeslug_sanitize_hex_color',
) );

$wp_customize->add_control(
  new WP_Customize_Color_Control( $wp_customize, 'core_color_setting_id',
  array(
    'label' => __( 'Core Color Setting' ),
    'description' => __( 'Select a color for something' ),
    'section' => 'custom_section', // Add a default or your own section
) ) );

function themeslug_sanitize_hex_color( $hex_color, $setting ) {
  // Sanitize $input as a hex value without the hash prefix.
  $hex_color = sanitize_hex_color( $hex_color );

  // If $input is a valid hex value, return it; otherwise, return the default.
  return ( ! null( $hex_color ) ? $hex_color : $setting->default );
}