Hra

yes, you can enter into an agreement and pay rent to your father (he should be owner of the property) and then claim HRA. 

I guess this comes as self occupied

Besides rent agreement, it will be beneficial for you, in case of notice by A.O (chances of which are less than 5%), if u can have the rent receipts, rent payments through net banking or cheque to substatiate ur payments & file ITR of ur father by showing the rental income in his return, else ur choice..

you can claim HRA for rent paid to your father, he must be the land lord of the place you are residing