What is the religious ruling on a questioner's refusal to bear the expenses of his father's 'Umrah, given the presence of other siblings who live with him and benefit from family properties, while the questioner lives in rented accommodation and his family is in need of money?

If the father is unable to perform Umrah due to lack of funds, the children are not obligated to finance his Umrah, because acts of worship are conditioned upon ability. However, if the father requests funds for Hajj or Umrah from his capable child, fulfilling his request falls under the commanded act of filial piety, and thus becomes obligatory from this perspective, unless it harms the son and his family, in which case abstention is permissible. If the father specifically asks you, and not your siblings, this is a blessing and a bounty, and you can agree with your siblings to pay a portion of the amount. It is recommended to strive in honoring one's father and not to be stingy with him in a way that does not cause harm, for honoring him is one of the greatest acts of nearness to Allah.