No. In the ABO blood type system, a parent with the blood type O and a parent with the blood type B can not have a child with the blood type AB.
A person with blood type O has no A or B antigens on the surface of their red blood cells. A person with blood type B has a B antigen on the surface on their red blood cells. Neither parent has the gene to code for antigen A so the child of both parents would not be able to have a blood type involving the A antigen, such as blood types A or AB.A father with O blood type is likely not the father of an AB child (+ or -) with a B- mother.
But blood tests for paternity are not 100% certain. In addition, people often mis remember their blood type.
The best paternity test is a DNA test.