The farmer had two sons. The first was born when the farmer was still young, and grew up as a handsome strong young man

The farmer had two sons. The first was born when the farmer was still young, and grew up as a handsome strong young man, whom his father was very proud of. The second, born much later, grew up a sickly child, and neighbors urged the farmer to file an application with a state court to establish paternity. The basis for the suit should have been the fact that, as the father of such a young man as his first son, the farmer could not be the father of such a weak creature as the second.
Blood groups of family members were as follows: farmer – IV blood group; mother – I group; the first son is group I, the second son is group III.
Is it possible on the basis of these data that both young men are the sons of this farmer? What are the genotypes of all members of this family?

No you can not. One and not a farmer’s sons, and this is the first son. The farmer’s blood type is IV, and his son could not have a group in any way.