Yes, you can get a Gift Deed or Will from your grandmother to protect your welfare after the death of grandmother. Your right in the properties of your father is also protected and after his death you are entitled for half share in his properties. The law is as follows:
What does the grandparent's property law in India state? Does the grandson own the right to the property?
All property's owned by a Hindu person devolves onto his class one legal heir's.
Now to the specific scenario's in ur example (for sake of convenience I'm presuming ur ur grandfather has only one legal heir)
Senario1: The property is self acquired by your Grandfather, in such case upon his demise interstate (without a will) the property would devolve upon ur Father and not you. In case your farther passes away before your grandfather then it such case it would be devolve upon you, your mother and ur siblings equally.
Scenario 2: the property in question is self acquired by ur grandfather father ( ur great grand farther) - would devolve same as scenario 1.
Scenario 3: the property in question is self acquired by ur grandfather grand father ( ur great great grand farther) - would devolve same as scenario 1.
Scenario 4: the property in question is self acquired by ur grandfathers great grand father ( ur great great great grand farther) - then in such a case you would be entitled to the property by birth as it becomes ur ancestral property.
To give you more clarity on the concept of Ancestral Property's : any property which passes undivided down 4 generations of male lineage is called ancestral property. The right to such property acures at birth unlike other laws of inheritance where right arises upon the death of the the owner.
Hope this brings some clarity to your question and your sense of entitlements.
HINDU WOMENS PROPERTY…. HOW IT DEVOLVELS
A hindu woman holds the property as an absolute owner and now she can dispose off the property as her own property. The concept of ancestral property does not apply to a property held by a hindu woman. Your maternal grandmother (naani) can will the property to anyone. However, if she dies intestate (without a will) then the property will devolve as per the rules of succession in Hindu Succession Act, specifically, section 15. In that case, the property goes to the legal heirs of the woman on her father’s side if she received the property from her father’s side and to her husband’s side if she received the property from her husband side.