Hi, thank you for asking Healthcare Magic.
HBsAG positive means you are infectious (acute or chronic).
Anti HBc antibodies
indicates previous or ongoing infection (once infected, it remains positive for life)
This means that an infected person (acute or chronic) must be positive for both of them. So, your case seems not to be conclusive. Either HBsAG came out falsely positive or Anti HBc antibodies came out falsely negative. In my opinion, I would suggest you redo the tests.
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I wish you good health