The Verdict: Not eligible
Emirati nationality passes only from a parent, so an Emirati grandparent or earlier ancestor does not give you a claim. If one of your parents could have been registered as Emirati and was not, that parent is the person to look at first.
Article 2 of the Nationality Law confers citizenship at birth through a father, or in limited cases a mother, who is Emirati. There is no grandparent route. The only historical clause, for Arab families settled in an emirate since 1925, required residence that continued until the law came into force in 1972. Claiming membership of a family or tribe you do not belong to in order to obtain nationality is a crime punishable by up to ten years in prison (Article 44).
What else might work: if your father was the son of an Emirati man and was himself born Emirati, he may be able to register first, and you would then follow under Article 2(b). Otherwise, the UAE offers long residence rather than citizenship, and our Golden Visa, Skilled Migration and Retirement quizzes for the UAE cover it.