Is it permissible to pay money to a person who helps in finding a job, knowing that this person has connections in the government and demands money in exchange for his help?

If a job is rightfully yours, and no one else has a claim to it, and you are competent for it, and you cannot obtain it except by paying a bribe, then there is no harm in paying it to secure your right. The person who demands the bribe is advised to make it purely for the sake of Allah the Almighty.