Hi,
your post is confusing. you can assign authorization group to a table in SE11 or SE54.Not sure what you need to do regarding transactions. regarding your custom table ZFI003. If users are going to use standard transactions to access this table (e.g. SE16) then access is controlled with object S_TABU_DIS. So you need to assign authorization group to this table. SE16 will then automatically perform checks for this group.
Cheers