add_settings_field() │ WP 2.7.0

class ClassName {

	public function __construct() {
		add_action( 'admin_init', [ $this, 'your_function' ] );
	}

	function your_function() {

		add_settings_field(
			'myprefix_setting-id',
			'This is the setting title',
			[ $this, 'myprefix_setting_callback_function' ],
			'general',
			'default',
			[ 'label_for' => 'myprefix_setting-id' ]
		);
	}

	function myprefix_setting_callback_function( $args ) {
		echo 'Content here';
	}
}

$ClassName = new ClassName();

A checkbox settings field can be checked on the front end by simply looking for isset. No need to add additional checks like 1, 0, true, false… . if a checkbox is not set then it returns false.

add_action( 'admin_menu', 'add_option_field_to_general_admin_page' );

function add_option_field_to_general_admin_page() {

	// settings checkbox
	add_settings_field(
		'wpdevref_removestyles_field',
		esc_attr__( 'Remove Plugin Styles', 'wpdevref' ),
		'wpdevref_removestyles_field_cb',
		'general',
		'default',
		[
			'type'         => 'checkbox',
			'option_group' => 'wpdevref_options',
			'name'         => 'wpdevref_removestyles_field',
			'label_for'    => 'wpdevref_removestyles_field',
			'value'        => (int) ( get_option( 'wpdevref_options' )['wpdevref_removestyles_field'] ?? 0 ),
			'description'  => __( 'Check to remove preset plugin overrides.', 'wpdevref' ),
			'checked'      => get_option( 'wpdevref_options' )['wpdevref_removestyles_field'] ?? 0,
			// Used 0 in this case but will still return Boolean not[see notes below]
			'tip'          => esc_attr__( 'Use if plugin fields drastically changed when installing this plugin.', 'wpdevref' ),
		]
	);
}

/**
 * switch for 'remove styles' field
 * @since 2.0.1
 * @input type checkbox
 */
function wpdevref_removestyles_field_cb( $args ) {

	$options = get_option( $args['option_group'] );

	$value = $options[ $args['name'] ] ?? null;

	// Could use ob_start.
	$html = '
	<label title="{TIP}">
		<input id="{ID}" name="{NAME}" type="checkbox" {CHECKED}/>
		<span class="wndspan">{DESCRIPTION}</span>
		<b class="wntip">?</b>
	</label>
	';

	$html = strtr( $html, [
		'{TIP}' => esc_attr( $args['tip'] ),
		'{ID}' => esc_attr( $args['name'] ),
		'{NAME}' => esc_attr( $args['option_group'] . "[{$args['name']}]" ),
		'{CHECKED}' => $value ? ' checked="checked" ' : '',
		'{DESCRIPTION}' => esc_html( $args['description'] ),
	] );

	echo $html;
}

and checking to render action on the front side would use:

// Options getter could be a function with arguments.
$options = get_option( 'wpdevref_options' );
$value = $options['wpdevref_removestyles_field'] ?? '';
if( ! $value ){
	// Do some
}

Optionally you can add a ‘false’ into any conditional( empty, null, ”, 0 ) .

myprefix must be unique, for example with some prefix of your plugin or theme. Also, let's pass the last parameter where we specify id and option name for the corresponding tag attributes:

<?php

add_action( 'admin_menu', 'add_option_field_to_general_admin_page' );

function add_option_field_to_general_admin_page() {

	$option_name = 'my_option';

	// register the option
	register_setting( 'general', $option_name );

	// add a field
	add_settings_field(
		'myprefix_setting-id',
		'Option Name',
		'myprefix_setting_callback_function',
		'general',
		'default',
		[
			'id'          => 'myprefix_setting-id',
			'option_name' => 'my_option'
		]
	);
}

function myprefix_setting_callback_function( $val ) {

	$id = $val['id'];
	$option_name = $val['option_name'];
	?>
	<input
		type="text"
		name="<?= $option_name ?>"
		id="<?= $id ?>"
		value="<?= esc_attr( get_option( $option_name ) ) ?>"
	/>
	<?php
}

As a result, on the "general" page, at the very end, we get a new fully working option: