If a mother had a child with her own son, could a paternity test yield positive result for the son's father?
Let's approach some different methods of distinguishing parents:

1: The Y chromosome. These are passed down from father to son. Therefore, if the baby is male, its Y chromosome will be the same as John's and his father's - it will be indistinguishable who it's from.

2: The X chromosome. A male baby always has one of the mother's X chromosomes. A female baby always has its father's X and one of the mother's X. A male baby of John and Mrs B would always end up with one of Mrs B's X chromosomes, meaning that this can't distinguish the father. A female baby would have two X chromosomes from Mrs B (because John's own X came from her), proving that it is the product of incest.

3: Mitochondrial DNA. mtDNA is passed on from mothers to their children, never from the father. Therefore regardless of whether John or Mr A is the father, the baby would have Mrs B's mtDNA - not useful.

4: DNA fingerprint. This is primarily based on stretches of the human genome that contain repeats of short DNA sequences (so-called STR/short tandem repeats, or VNTR/variable number tandem repeats). In both cases, the sequence is the same in individuals, but the number of repeats is extremely variable and each human therefore has a (possibly) unique combination across the different repeat locations in the genome. Because children inherit 50% of their DNA sequences from the father and 50% from the mother, John himself will have his mother's characteristic lengths in 50% of repeat locations and his father's in the remaining 50% of locations (roughly). A child of John and Mrs B would have MrA's repeat lengths in 25% of locations and Mrs B's in 75%. The fractions "100% Mr A" vs. "50% Mr A" vs. "25% Mr A" can be distinguished by this method.