Shaidai or Shaidayee (Shai-daa-ee) is an Urdu word which means someone who is infatuated (with something or someone).
In the song 'Rabba' of Mausam (the version sung by Rahat Fateh Ali Khan), the word Shudai also seems to be the same as there is no word Shudai, known at least to me. Any further knowledge about that one would be welcome.