Advanced Custom Fields – category image

Whenever in doubt, consult the documentation and nice plugins like ACF are very well documented.

It depends on how you set the image field, but from this page Field Types -> Image, looks like you set you field to return an object.

Instead of using the_field, which prints the value, you need get_field:

$category_image = get_field('cat_small', $linkedcat);

And then:

$image = $category_image['url'];

Or, if available:

$thumb = $category_image['sizes']['thumbnail'];

Also, instead of echo, use var_dump to debug arrays.