How can I set the permission for a document or library such that the user (or user group) can read only the current version of the document and have no access to older versions.
there is an old post which contains the answer to your question.
As you might already know Sharepoint comes with default user groups. You've not stated whether you want users to only view documents or whether they also need to edit documents. This affects your next step.
I will assume you only want users to view and not edit. Therefore create a new group based on the View Only permission level, configure the new group (let's call it View-Not_Versions), but simply do not select the
View Versions permissions.
As you see from the link a 'Permission Level' is a modular, cumulative way of building permissions. The View-Not_Versions group will behave the same as the OOTB View Only permission, except users will not be able to view versions.