I have a class similar to:
public class MyClass : MyBaseClass
{
        public string Field1 { get; set; }
        public string Field2 { get; set; }
        public string Field3 { get; set; }
        public string Field4 { get; set; }
}
public class MyBaseClass
{
        public string BaseField1 { get; set; }
        public string BaseField2 { get; set; }
        public string BaseField3 { get; set; }
        public string BaseField4 { get; set; }
}
I then created a method to pull the names from the class.
private void MyMethod<T>(List<T> listData) where T : class
{
    String[] fieldNames = Array.ConvertAll<PropertyInfo, String>(typeof(T).GetProperties(), delegate(PropertyInfo fo) { return fo.Name; });
    // Do something with the fieldNames array....
}
So when I get my array it would be in the following order:
Field1
Field2
Field3
Field4
BaseField1
BaseField2
BaseField3
BaseField4
I was wondering if it was possible to change the order so that the base class fields were first followed by the derived class fields?
Let's implement a simple method to get how deep is the class in the class hierarchy
null <- object <- ... <- MyBaseClass <- MyClass <- ...
Implementation
// 0     - null
// 1     - object
// ...
// n     - MyBaseClass
// n + 1 - MyClass
// ...
private static int TypeLevel(Type type) {
  if (null == type)
    return 0;
  return TypeLevel(type.BaseType) + 1;
}
And then with a help of Linq sort by this criterium, the only little trick is to use DeclaringType - where (in which class) the property has been declared:
// fieldNames are actually properties' names
string[] fieldNames = typeof(MyClass)
  .GetProperties()
  .OrderBy(p => TypeLevel(p.DeclaringType)) // <- base first, derived last
  .ThenBy(p => p.Name) // <- let's organize properties within each class
  .Select(p => p.Name) 
  .ToArray();
Console.Write(string.Join(Environment.NewLine, fieldNames));
Outcome:
BaseField1
BaseField2
BaseField3
BaseField4
Field1
Field2
Field3
Field4
Finally, your method can be something like this:
// we don't want any restictions like "where T : class"
private void MyMethod<T>(List<T> listData) {
  ...
  string[] fieldNames = typeof(T)
    .GetProperties()
    .OrderBy(p => TypeLevel(p.DeclaringType)) // <- base first, derived last
    .ThenBy(p => p.Name) // <- let's organize properties within each class
    .Select(p => p.Name)
    .ToArray();
  ...
}
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