You are a child who has been prophesied by fate.
You are to demigods what demigods are to humans. You could, with great effort, be able to damage the gods and those who are immortal, though you find it easier to harm those who are divine in nature. The connection that you have gained to your divine parent has been enhanced, similar in nature to other prophesied children such as Percy Jackson or Piper, to name the most notable examples.
Simply put, you have greater access to the domains of your godly parent, being able to access more than a normal demigod. For example, if you happen to be the child of Poseidon, you would be able to cause earthquakes and thunderstorms and even manipulate elements farther away from water, such as blood and poison that comes from divine sources. Or if perhaps your godly parent had been Hades, you would be able to call upon more skeletons. Dredge up valuable materials from under the earth and place Curses upon your foes.
The gods fear you as you have the potential to overthrow them, similar to how Kronos betrayed his father and Zeus betrayed him. You have gained the potential to become closer to the divine as you age, with your divine blood strengthening and becoming more potent with time, furthering your legend.