I bought the house of my father three years ago and I have paid half of the amount. After that my father died and now I want to pay the rest to my mother. I don't know if I am on the right side. Please answer me as soon as possible

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

If contract of sale is done and half of the value is paid, then the house is yours. The remaining part of the value becomes property of inheritors and you are of them.
So, such a property should be distributed between inheritors each according to his/her right. In other words, the value of the remaining part should not be given to your mother unless your father deputized your mother to be a guardian of minor inheritors or the adult inheritors cede their rights.
Allah knows best.