I don't want my sister to apply for the same position as me
Why is it that you don't want your sister to apply for the same position as you?
Because we already compete enough. I don't want to do it at work, too.
That is your sister's business. She can apply to whatever job she wants. Try showing her other places to apply that are just as good as your place of work.
I've been doing a lot of work and it will be unfair if they select her.
While you shouldn't try to tell your sister what she can do in her career, it also seems like it might be for the best if you don't apply to the same places. Maybe you can talk to her and find a compromise.