Community users don't have edit button on case comment created by themselves in customer service community.
Community user profile has read,create,edit access on case. OWD for case is Private for both Internal and external users.
I checked in profile and there is no app/system permissions to enable edit access on case comments. I also checked in profile by disabling enhanced profile view but still I could not find this permission.
Updating an existing CaseComment is restricted
In the Salesforce user interface, comments are generally entered by a User working on a Case. All users have access to create and view CaseComment in the Salesforce user interface and when using the API. In the API, CaseComment records can't be modified after insertion unless the user has the “Modify All” object-level permission for Cases or the “Modify All Data” permission. If not, users can only update the IsPublished field, and can't delete CaseComment.
If you think about the way Salesforce's own Support works, once you make a comment on a case, you can't edit that comment, you need to make a new comment.
