If the kitten is alone for a day like that, then the kitten is essentially "abandoned", or is lost or homeless. Many things may have happened. The mother may have been trapped and taken. The kitten may have been dumped. It's unlikely the kitten would be naturally away from it's mother by choice, being so small.
The kitten definitely needs care. Food, fresh water, shelter and protection from predators. If your mother won't provide that and there's no one shelters, it's difficult to know what to advise.
You say you have an exam. I don't know if you're at school, or a higher college or university, you could always put up a notice for someone willing to take the kitten. Negotiate with your mother, that you could look after her until you find her a home. Or take it to school and see if there's a responsible adult who will take it.
If your mother won't let her into the house, then provide a box with a towel in a sheltered area, with a bowl of water and food. This kitten will need to be fed before you leave, when you return and before you go to bed. Preferably, it would be good to lay down some kitten dry food for the in between times for her to snack. Being outdoors, without supervision, it's more than likely that any food left out for her will be eaten by other animals.
If there is any local vet arrange to have the kitten taken to the local vet. At least they can care for it.
Just be warned, the kitten is vulnerable outside and at a high risk of poor health or dying without protection and care. She will need to be wormed and vaccinated and is prey to dogs and any other local native carnivores, including birds. She has not eaten enough in the last day at the very least and if not taken care of could also starve to death. The longer she goes without the proper care, medicine, nutrition the less chance she has of surviving.
Try and convince your mother to take the burden of responsibility of making this kitten safe. Good luck and let us know how you get on.
Update: from your comment.
about her size she's three times my palm size,today I gave her some
tuna & water..she didn't drink enough water considering how hot today
is,also noticed that she can't see me completely & her eyes are blurry
( respiratory infection?)she is walking slower.
This kitten needs urgent Veterinary care. She is sick and will die without medical treatment. You haven't done anything wrong, she would be worse off if you hadn't fed and watered her.
She needs to be taken to a Vet immediately. She is very young and sick. She is deteriorating and will die without seeing a Veterinarian. I'll repeat, the longer she goes without the proper care, medicine, nutrition the less chance she has of surviving.
