Can a person having hepatitis B antigen negative donate blood?

it's highly doubtable, just go to a donating place and ask

Hepatitis B antigen tells you whether or not you are infected with the virus.  You want that to be negative.  

When you get the hepatitis B vaccine you are supposed to get hepatitis B antibodies.  So you want to be hepatitis B antibody positive.  The hepatitis B vaccine is a 3-shot series.  After you finish the series, you should be tested if it worked and you have the antibodies.  This is what tells you if you are protected against the virus.  Sometimes people need to get the vaccine series more than once to get the antibodies, which is probably the case with you.

When you donate blood, they will always test your blood to see if you have ever been exposed to the hepatitis B virus.  If you have never been exposed, they will accept your blood.  If you have been exposed at some point, then they will contact you and let you know that they cannot use your blood.