We find a new general black hole solution in the braneworld scenario, considering a modified 5-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>f</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>ℛ</mml:mi></mml:mrow></mml:mfenced></mml:math>action in the bulk. We study the horizon structure and find the possibility of two, one, or no horizon depending on the value of the topological parameter<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>β</mml:mi></mml:mrow></mml:math>. On the thermodynamics side, we show that the value of the topological parameter determines the black hole temperature to have a divergent behaviour at small scales or to present a maximum value before cooling down towards a zero temperature remnant.