My father passed away and left me his house in his will. I’ve now registered it in my name. Will it still be considered inherited property? If I choose not to give my children any share, can they legally claim any part of it?

Yes, the house will still be considered inherited property, even after registration in your name. While you can exclude your children from your will, they can legally challenge it based on their right to maintenance under the Hindu Succession Act, if they prove dependence on you.