public class BaseDto
{
    public int ID{ get; set; }
}
public class Client: BaseDto
{
     public string Surname { get; set; }
     public string FirstName{ get; set; }
     public string email{ get; set; }
}

PropertyInfo[] props = typeof(Client).GetProperties();

Type type = typeof(Client);
List<Type> types = new List<Type>();
do
{
    types.Insert(0, type);
    type = type.BaseType;
} while (type.BaseType!=null);

PropertyInfo[] props = typeof(Client).GetProperties()
                                      .OrderBy(x => types.IndexOf(x.DeclaringType))
                                      .ToArray();

typeof(Client).BaseType

BindingFlags.DeclaredOnly

var baseProps = typeof(BaseDto).GetProperties();
var props = typeof(Client).GetProperties();

var allProps = baseProps
   .Concat(props.Where(p => baseProps
      .Select(b => b.Name)
      .Contains(p.Name) == false));

Dictionary<string, PropertyInfo> _PropertyIndex = new Dictionary<string, PropertyInfo>();

Type thisType = typeof(Client);

foreach (PropertyInfo pi in thisType.BaseType.GetProperties())
    _PropertyIndex.Add(pi.Name.ToUpper(), pi);
foreach (PropertyInfo pi in thisType.GetProperties())
    if( !_PropertyIndex.ContainsKey(pi.Name.ToUpper()))
        _PropertyIndex.Add(pi.Name.ToUpper(), pi);