You cannot stop puberty because all people in the world experience puberty,you cannot stop it because your body is changing from being child to teenage and next to adulthood.Don't feel afraid about it,just enjoy that stage and have fun.
Now, if a girl starts puberty very very early (like starting her period at age six), a gynecologist can put her on medication (i've forgotten the name of it, sorry) to stop it for a few years, because once puberty starts, it slows down/halts a girl's growth.
But other than an extreme reason like that, no. If you mean just stop the period, there are various methods of birth control that will reduce the number of periods you have.
The only way to suppress puberty in male and female is to control what and how they experience life. I.e. The tv they watch and the people they talk to, as they grow an learn what life is about puberty begins to kick in