The problem with your toilet is called: Fuild Master, this is the water valve inside the tank, it is the part that goes through the whole on the corner of the toilet and connects with the water supply line in the bottom of the tank.
According to what you describe, the part is deffective and must be replaced.
You can buy a new fluid master at Home Depot or any other plumbing supply store. It usually cost around $10 to $20 and you can easily replace it yourself.
Make sure that, before you remove anything, shut the off and flush all the water from the tank.
Once you've done that, with a channel lock or wrench unscrew the supply line from the bottom of the tank then, while holding the old fluid master inside the tank, unscrew the nut from unter the tank.
Remove the old fluid master and follow the directions to install the new one in the tank.
Also, consider checking the water supply line to make sure that, it is long enough, otherwise, it might leak, you might need to replace the supply line, which is also very cheap.
Once everything is installed, and the tank is full, make sure that the new fluid master height is adjusted accordingly, the water must be at the right level, please, see the water line mark in the tank wall.
Also, check for leaks, if everything is ok, you're good to go.
Sincerely,
Joe
Remember: The information provided here is for informational purpose only, if you're not sure how to do it, consider hiring a professional, otherwise, do it at your own risk and discretion.