How can I deal with my unjust father who falsely accuses me and refuses to discuss it?

You must honor your father, treat him with kindness, obey him in what is right, and associate with him in a good manner, even if he is unjust, as Allah Almighty says: "And We have enjoined upon man [care] for his parents - good treatment" (Quran 46:15) and "And accompany them in [this] world with appropriate kindness" (Quran 31:15). Do not be annoyed by his accusations against you, and be patient. If you treat him well, he will be pleased with you, and Allah will be pleased with you. Remember the saying of the Prophet, peace and blessings be upon him: "May he be humbled who reaches old age with either one or both of his parents and does not enter Paradise." You can ask some righteous people to mediate and mend the relationship between you.