I need search in One custom Category

The search function is called with the “?s=” query. So maybe simply modifying the form will do what you want (I mean it works, I just don’t know if it’s what you’re after looking for):

<form method="get" id="searchform" action="http://www.domain.com/category/myspecialcat/">
<input type="text" value="<?php echo wp_specialchars($s, 1); ?>" name="s" id=s>
<input type="submit" id="searchsubmit" value="Search My Special Cat">
</form>