You're after the exp:assets:files template tag:
{exp:assets:files folder="{filedir_1}public"}
<li>File name: {filename}</li>
{/exp:assets:files}
Change {filedir_1} to whatever is appropriate for your Assets field.
To find what your filedir id is, go to Content → Files → File Upload Preferences and hover your mouse cursor over the appropriate "Edit" icon for the directory.
Within your browsers status bar, you will see "id=X". Use this number within {filedir_X}, for example in my screenshot mine is {filedir_1}.

Note: It's not clear in your answer, but if your "Server Path to Upload Directory" is set to something like /home/me/www/assets/docs" and you've created the "public" directory within Assets. Then your correct folder path to 'public' is: folder="{filedir_1}public"