neighbors want structures demolished or pay them P10,000 monthly rent

our neighbors claim they own half the lot area where our ancestral house stood. the feud has been going on since time immemorial and we have always been telling them that we are willing to pay whatever land area our family might have unintentionally occupied. the story is so complex and long, but the gist is that the survey results showed we indeed occupied their lot. now, the neighbors say they want all structures demolished or we pay them monthly rent of P10,000. the problem is that they have no land title to support their ownership claims, but only a few unimportant documents. one of them even arrogantly declared as if to threaten us that she works in the neighboring city's assessor's office. are their demands legally possible? what legal options do we have? thank you in advance for any legally insightful information you could share. godbless.