Can a AB poitive mother and B negative father have O positive kid?

No, this is not possible for an AB positive mother and a B negative father to have an O positive child.

For a child to have O positive blood type, both parents must contribute an O allele. The mother can only contribute an A allele or a B allele, while the father can only contribute a B allele or an O allele. Therefore, it is not possible for them to have an O positive child.