使用复合主键作为外键

is wrong. You can't use pk_studentID like that, this is just the name of the PK constraint in the parent table. To use a compound Primary Key as Foreign Key, you'll have to add the same number of columns (that compose the PK) with same datatypes to the child table and then use the combination of these columns in the FOREIGN KEY definition:

CREATE TABLE files
(
  files_name varchar(50) NOT NULL, 

  batch_id varchar(4) NOT NULL,         --- added, these 3 should not
  dept_id varchar(6) NOT NULL,          --- necessarily be NOT NULL
  student_id varchar (25) NOT NULL,     --- 

  files_path varchar(50),
  files_data varchar(max),              --- varchar(max) ??   
  files_bookmarks xml,                  --- xml ??
                                        --- your question is tagged MySQL, 
                                        --- and not SQL-Server

  CONSTRAINT pk_filesName 
    PRIMARY KEY (files_name),

  CONSTRAINT fk_student_files                     --- constraint name (optional)
    FOREIGN KEY (batch_id, dept_id, student_id)  
      REFERENCES student (batch_id, dept_id, student_id)
) ENGINE = InnoDB ;

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