Knowing that you get one chromosome from your mom and one from your dad, you can figure out what the possible blood type is. People with blood type A can have either two A chromosomes (AA), or one A and one O chromosome (AO). Since we already know you are type O, then the father must be type A. If you find out the supposed father is not type A and you are sure about everything else, then this person is not your daughter.
The Father can have two blood types. Type A from the combination AA or AO. He could also be type AB.