Child with blood group O has B group father. The father has a genotype of

The correct option is B $I^O{I}^B$
The father with B group can have the genotype $I^O{I}^B$ or $I^B{I}^B$ . The child with blood group O will have the genotype ii, one from each parent. Hence the father has the genotype $I^O{I}^B$.