I am looking for plugin or is there any method/function to create user groups and give an access them to modify/access.
You'd use roles for this. You'd create a new role that has the required access and then assign anyone you want to be in that role 'group'.
The User Role Editor plugin should give you the functionality you need to create the access you require.
I believe this is what you are looking for: Groups
I have used User role Editor in the past to accomplish custom role permissions. It worked well for my use case allowing me to assign permissions to groups or individuals as need be.
Compatibility may be an issue with certain plugins but I didn't experience any issues.