What rights do you have as the only child of your father who was remarried and had no will but is deceased now?

You need to consult with an attorney who specializes in probate in your jurisdiction who can review your situation and explain your options. It may depend on how the real estate was titled. If the property was in your father's name then you may be entitled to a share. His estate must be probated. If there is no will that can be found then an administrator must be appointed by the court. You need legal advice from a professional who knows all the facts, can check on the title of the real estate and can apply the laws in your state.