Most likely the referenced mineral interest is your fractional share in the 62.9803 acres. Generally the minerals are divided among heirs and purchasers over the years. For example if A owned 100% and had 10 children who got equal share, then each child would own 1/10. If A owned 100% and sold 1/2 of the minerals at some time, then the 10 children would each get 1/10 of 1/2 = 1/20. Ask the oil company to confirm what is meant by Mineral Interest.