Is it permissible to work under a government employment contract obtained through nepotism, knowing that this contract is designated for those whose contracts were canceled in 2005, and that obtaining previous entitlements is not my right?

If the responsible authority accepts your inclusion among the youth without deception, bribery, or trickery, there is no harm in you accepting that. The money given without work is considered a gift, and there is no harm in accepting it. However, if there is trickery or deception from the officials to include you among the beneficiaries of those contracts without the knowledge of the decision-making body, then it is not permissible for you to accept that or take the money.