It appears that your deceased father owned a property to which you and your lone sister are the successors. (you have not mentioned anything about your mother. If she is surviving then she too will have equal share).
It also appears that you want to be the sole owner of the property by getting transferred the share of your sister to you. There can be a 'release deed' relinquishing her rights in the property in your favour or a 'family settlement deed' having the same effect, depending upon the state in which the property is situated.
If you want to pay money to your sister, as per your mutual agreement, for execution of any of the said two deeds, then it will be 'sale' / 'conveyance' attracting stamp duty on the amount paid or guidance value of your sister's share in the property, whichever is higher.
Your issue appears to be that money is involved, hence a sale deed is to be executed. But you don't have the money on hand and need bank finance.
Solution: Get an agreement of sale executed by your sister, agreeing to transfer her share in the property for the specified 'consideration' (amount). Then you approach the bank for finance. Then it will be a simple loan transaction for the purpose of purchase of a property.
Note: You have used the word 'property' in your query, which is a wide-ranging word. Instead, the simple word 'house'/'flat' should have been used, for providing clarity, which point, is deduced by me from the use of another expression, 'staying in', in your query.