What is the ruling of Islamic law on paying a sum of money to a witness to testify that I did not run a red light, in order to prove my innocence in a traffic accident and receive compensation, especially since the court ruled both parties innocent due to lack of evidence?

It is not permissible to seek help from a witness who testifies to something he did not see or know in order to establish the truth, for this is a false testimony (shahadat az-zur) forbidden by Islamic law, even if the intention is to reach the truth. The Prophet, peace and blessings be upon him, warned against false testimony and considered it one of the gravest major sins.