Since you are using comments_template() function to display comments, it internally calls comments.php file of your theme.

In comments.php file, you should have a function wp_list_comments() with some parameters. You have to add one more parameter per_page in that function, as follows :

wp_list_comments( array(
                       'style'       => 'ol',
                       'short_ping'  => true,
                       'avatar_size' => 56,
                       'per_page' => '3'
                       )              
                );

This worked for me.

Since you are using comments_template() function to display comments, it internally calls comments.php file of your theme.

In comments.php file, you should have a function wp_list_comments() with some parameters. You have to add one more parameter per_page in that function, as follows :

wp_list_comments( array(
                       'style'       => 'ol',
                       'short_ping'  => true,
                       'avatar_size' => 56,
                       'per_page' => '3'
                       )              
                );