In the page with the Query :
$QUERY = "SELECT * FROM company WHERE comp_name LIKE '$letter%' ORDER by comp_name";
In your page with the letters, just write something like:
<a href='page_with_query.php?letter=A'>A</a>
<a href='page_with_query.php?letter=B'>B</a>
<a href='page_with_query.php?letter=C'>C</a>
But before making the $Query = ..., make a validation (make sure the $letter var is one caracter only and is a character.)