Remove specific theme from WordPress Core Updates.

functions.php

<?php
// remove specific theme from WordPress Core Updates
add_filter('site_transient_update_themes', 'ndt_remove_theme_from_transient_update_themes');

function ndt_remove_theme_from_transient_update_themes( $transient ) {

	if ( is_object( $transient ) && isset( $transient->checked ) && isset( $transient->response ) ) {

		$checked = $transient->checked;
		$response = $transient->response;

                // replace nictitate slug by your theme slug
		if ( isset( $checked['nictitate'] ) ) {
			unset( $checked['nictitate'] );
			$transient->checked = $checked;
		}

		if ( isset( $response['nictitate'] ) ) {
			unset( $response['nictitate'] );
			$transient->response = $response;
		}

		return $transient;

	}

	return $transient;

}