Can i lose a kg with having a fasting day on apple or watermelon and not gain that 1 kg fat again?

Yes & no: I assume you're not 100 years old as noted in your profile. Regardless, yes, you might be able to lose a kg by fasting but that would most likely be water weight. So in answer to 2nd part of your question, no, you'd probably regain weight once you started eating/drinking normally again, although it wouldn't be fat weight per se. Best to eat sensibly each day, aiming for 500cal/d less eaten = 1#/wk.