I bought a car and agreed on a certain amount with the owner. When we disputed he said his father is the one who will settle the case. I am satisfied with him being the judge because he is an Imam of a Mosque. He said a certain figure which I agreed to, but after some time he came back and told me that he wants an addition to the agreed figure. Should I pay that extra money even though I don’t have any? إذا تم البيع فلا حق للمتعاقدين بعده في شيء

Praise be to Allah, and may Allah’s peace and blessings be upon the Messenger of Allah, his family and his companions.

To proceed:

In response to your question, we say, and with Allah Almighty lies all success:
According to what I understood from your question, you should not give him anything because he took the money you agreed upon on the contract and he was pleased with it. Allah the Exalted says: “whereas Allah has permitted trading.” [al-Baqarah: 275].
He (Allah) also says: “O you who believe! Eat not up your property among yourselves unjustly except it be a trade amongst you, by mutual consent.” [al-Nisaa’: 29].
In a hadeeth narrated in Sunan with a sound chain of narrators the Messenger of Allah (peace be o him) said: “Transactions may only be done by mutual consent.”[1] And in your case there is mutual consent so
the seller has no right of coming back and asking for more. For instance, after the contract has been concluded, a man has no right to request anything if he had consented to the contract. If this was not the case then dealings were going to be chaotic. Therefore he does not have any right over you, but if you wish to please his heart by being generous to him, then that will be from your own good but it is not compulsory on you.