A handwritten will is legally valid even without a notary, but only under certain conditions. The key thing is that the document must have the testator's own signature, the date, and the place where it was made. If all that's there, such a will is considered valid. However, it can be contested if you can prove that your father wrote it under pressure, under duress, or that he wasn't of sound mind. Also, a will can be contested if violations of its form are discovered - say, the signature is forged or the date is made up.
If the will is found invalid or if there is no will at all, inheritance goes by law. Then the property is divided equally between the spouse (your mother) and the children - that is, between your mother and you. Each gets half. That's a lot fairer than if everything went to one person based on a handwritten document of questionable authenticity.
To sort out your specific situation, you need to show the will to a lawyer - preferably two, to get independent opinions. A specialist will look at the handwriting, the date, the conditions under which it was written, and tell you how vulnerable the document is to being contested. If you and your mother both doubt its authenticity, it makes sense to file a lawsuit - the court will order a handwriting analysis and figure it out on the merits.