Hi, I am 21 years old and I have a sister who is 13 years old. I live with my mom and my sister only. Lately my sister has started to fantasize all sort of adult things. By adult thoughts I mean is she is seeing me with another girl kissing her. She was sitting in the class studying and she had a desire to kiss her teacher on her lips. She is more onto getting thoughts related to kisses. I just don't know how to handle her. What to tell her. She confides with me only and is afraid of telling all this to mom. After she has these types of thoughts she feels bad and says I don't want to get these thoughts again, please help me. And I end up scolding her and shooing her away. Please do help me and guide her.

Has anyone explained the 'birds and the bees' to her ? If not perhaps it is time your mother sat her down and explained.

If you are so concerned, stop scolding her. It's time some one have a talk with her about sexuality. She is at the age where those thoughts creep in... puberty and all

She is just 13, it means her mind is not matured enough to understand what is good and what is bad. You are older than her and matured enough, so divert her mind from it by teaching her what she should do (like hard work, Study, Importance of pursuing the dreams, etc.)
Do not keep on telling her about what she should not because it is better to use positive words to explain any human mind. Create positive atmosphere around her and then give her some time. She will definitely throw out all those things.

Tell her that teen crushes on teachers are common, and teen crushes on the same sex are sort of common, so there's nothing wrong with her fantasies.
Let her know that she can confide in you about anything.
If she becomes obsessed, ask about this again, but give her plenty of time to go through this phase.
Telling her to get such thoughts out of her mind don't help, and actually can easily make her dwell on them more.
Distraction with other interests helps, whether it's a subject in school or a sport or hobby. But teens think about sex and romance, and that's normal.

She needs to talk to a mature adult, someone that can explain to her that at 13 sexual thoughts come and go, and don't mean anything. She doesn't have to feel bad about her thoughts. They're just thoughts.

She needs to be able to talk to someone that won't make her feel worse about her thoughts by shooing her away and scolding her

Right now you're her biggest problem because of the way you're reacting to her.

I just looked at your other posts.

Seems you have the same issue as your sister, sex is always on your mind as well.

You're in India according to your profile and other posts.

Sadly, in India, they don't council their youth on sex, there's no sex education at all. Teens that are confused by normal things, are made to feel dirty and bad because of their thoughts, and grow up as confused adults that have no idea that thoughts about sex is natural.

I don't now how we can help you with your sister when you can't even help yourself.