LINQ to Entities does not recognize the method 'System.DateTime Parse(System.String)' method, and this method cannot be translated into a store expression.

Well, that seems pretty straightforward:

// Note the changes from your code here
DateTime currentDate = DateTime.Today;
DateTime endDate = currentDate.AddDays(3);
DateTime dueDate = db.Files.Where(y => (y.DueDate >= currentDate) && (y.DueDate <= endDate) && (y.UserID == user.ID)).ToList().Take(7);

However, if, like I suspect, the DueDate property of the File object is not a DateTime but a string (as suggested by the code you wrote), I'm afraid you won't be able to do it in a single Linq expression. You will have to resort to a plain old foreach loop. Something like:

DateTime currentDate = DateTime.Today;
DateTime endDate = currentDate.AddDays(3);
List<File> files = new List<File>();
foreach (File file in db.Files) {
   DateTime dueDate = DateTime.Parse(file.DueDate);
   if ((dueDate >= currentDate) && (dueDate <= endDate) && (file.UserId == user.ID)) {
      files.Add(file);
   }
}
// Here you have you File collection.
files = files.Take(7);

Conclusion: when you have DateTime values, use the DateTime type, not the string one.