JSONArr := TJSONArray.Create;
  try
    FResourceCacheEdit.First;
    while not FResourceCacheEdit.Eof do
    begin
      if FResourceCacheEdit.Edited = True then
      begin
        JSONObj := TJSONObject.Create;


        JSONObj.AddPair(TJSONPair.Create(fnSCH_Name,                     'Тест 1'));         
        ...
        JSONObj.AddPair(TJSONPair.Create(fnSCH_Qualifications,            (TJSONObject.ParseJSONValue('[1,3,15]')) AS TJSONArray));

        // Сохраняем объект в массив.
        JSONArr.AddElement(JSONObj);
      end;

      FResourceCacheEdit.Next;
    end;

    Result := JSONArr.ToString;
  finally
    JSONArr.Free;
  end;

[  
   {  
      "Name":"Тест 1",
      
      "MainQualification":1,
,
   }
]