list all categories that have a certain word in title

How to list all the categories that have a certain word in title - first word of the category? in category.php

so, for example, if I am viewing the category "Green Apples Sells", it will list all the categories that start with the word "Green"

In addition to this rule, the listed categories must not have any children (if it has children don't list it, even if the first word matches) I was unable to find this anywhere on the web.

thank you