can baby have a different ANTIGEN blood type from the mum (NOT talking about Rh factor)?

Yes, a group A mother can have a group B baby.  However, the anti-B that she produces does not cross the placenta, therefore, baby is safe.

It is a bit different with group O mothers that have either a group A or group B baby.  They have anti-A and anti-B that don't cross the placenta (fetal-maternal barrier), but a group O mom additionally has another antibody called anti-AB that does cross the placenta and causes very mild neonatal jaundice, very minor in comparison with the Rh antibodies, which can be lethal to the fetus.

ABO antibodies are IgM, so the won't cross the placenta (IgG, such as anti-D (or anti-Rh) can).  During delivery, the exchange of fetal and maternal blood from the abruption of the placenta can cause a small mixing of the blood.  Keep in mind that the antibodies to the ABO antigens form in the first year of two of life, so the baby has no antibodies that would bind to the mom's red cells.

For some reason, maternal antibodies binding to the baby's cells is (in my experience, and that of others who I've spoken with) most commonly seen in type O moms and type A babies.  You could have one of 4 antibodies that bind to the cells in this case:  anti-A, anti-A1, anti-AB, anti-A1B.  The exact type can be determined via something called a Lui elution, though it is not important to know which--they all cause the same end effect of increasing red cell destruction in the baby.

There are other antigens on the baby's cells which could be processed by the mother's body if some of the cells entered her body during gestation.  She could (either ante- or post-partum) develop IgG antibodies to the antigens that were exclusive to the father and passed on to the child, but this is not common.