“I am writing a Children’s book. On the back cover, I have chosen to use a quote from someone else. For example; ‘ Today someone is sitting in the shade, because someone a longtime ago, decided to plant a tree’… Warren Buffet. Do I need to be concerned with permission or issues from using this quote on the cover of the book?”
The short answer is yes, but you should consult an attorney to address the specific quote you want to use and where it came from. Likely there is a copyright infringement concern here. Copyrights do not require that the material be registered; meaning almost any statement published by someone can be treated as a copyright for which they are protected against infringement. That is not to say that all quotes are, so please consult with an attorney.
Also, there are some limits on how long a copyright lasts, and again, you should consult an attorney to learn the limits that apply to the specific material for which you are inquiring.