Do I have usufruct of the home my mother and I purchased together even though my brother is demanding I sell it for his share.

If your brother is not on the deed, how does he have an ownership interest in the house? If he is not a co-owner he has no right to demand it be sold or a right to a portion of the proceeds. Were the funds used to purchase the home subject to a usufruct?

You will need to see a lawyer. The matter you pose is complicated and you have not provided enough information. For example, did your mother leave a will and are you listed on the title to the property. Her estate will have to be probated, if so. If she did not, her portion of the home will have to proceed through a succession. Without knowing more information, it appears that you are a co-owner and would have owned at least 1/2 the property together with your mother. Your brother's potential interest, if there are no other brothers or sisters, would be 1/2 of your mother's interest or 1/4 of the property, if you co-owned it with her. You, assuming your facts are correct, would have an interest in the other 3/4. Your brother would have to sue to divide the property after he has been put in possession of his portion of your mother's estate through a judgment by the court in the Parish where the property is located. Until he has been declared an owner which you would be at the same time, he has no right to force you to sell or evict you. At the very minimum, you would own 1/2 of the house, if you were not on the deed. There are many other issues that I have not begun to discuss and as you can see, you will need the advice of a lawyer in the Lafayette area.