Rent paid to dad - hra allowance claim

I do not think that your father has right to sub-lease the property.

Therefore, I do not think that you have any lease agreement with your father.

All that you are doing is that you are contributing to your father to meet part of the lease rent.  That will not mean that you are paying rent.

Since it is only a contribution, it is not income in the hands of your father.

Further, unless your father is in the business of leasing, and he has entered into any sub-lease agreement with you, he cannot treat the same as his business income.

If that be the case, then you can claim Rental payment against receipt in connection with your HRA.

In your father's hands, it will be income from house property.  He will be entitled to a deduction of 30% from the rental income received from you.  On the remaining balance, he has to pay income tax.