This is not possible by default. If you want to filter them, use collections instead.
But you could create a custom api endpoint and fiddle with the results:
// custom api endpoint in `/config/api/singletons/find.php`
// Your Singletons with a field named "title"
// Search all Singletons with the title "test"
// tested with SQLite - I don't know, if it works with Mongo, too
$options = [
'filter' => [
'val.title' => 'test',
$singletons = $this->storage->find('singletons', $options);