What is the ruling on receiving a father's pension while working in the private sector without insurance, and is this pension considered permissible or impermissible?

If the intent behind the question is to defraud the pension authority to receive a pension in the father's name, then it is forbidden, due to the deception and trickery involved. The Prophet, peace and blessings be upon him, said: "Whoever cheats us is not of us," and "Cunning and deception are in the Fire." This includes all forms of cheating and deception, especially if it pertains to the property of others or public funds. Money taken without right will be a burden upon its owner on the Day of Judgment. The fact that the questioner is not entitled to insurance due to her work in the private sector does not permit her to resort to deception. However, if she pursues legitimate means and the responsible authority approves of it, then there is no objection.