Use the glob function in a foreach loop to do whatever is an option. I also used the file_exists function in the example below to check if the directory exists before going any further.
$directory = 'my_directory/';
$extension = '.txt';
if ( file_exists($directory) ) {
foreach ( glob($directory . '*' . $extension) as $file ) {
echo $file;
}
}
else {
echo 'directory ' . $directory . ' doesn\'t exist!';
}