The idea of `Farr-i Izadi`, on which the Mughal kingship was based, was first developed by Shihabuddin Suhrawardi, according to the correct answer. Option 1, Shihabuddin Suhrawardi, is the correct answer to the question.

Now let`s analyze the other options to understand why they are not the correct answer:

- Option 2, Nizamuddin Auliya, is not the correct answer because he was a prominent Sufi saint in the Chishti order and his teachings focused more on devotional practices and social welfare rather than the ideology of `Farr-i Izadi`, which refers to the divine right of kingship.

- Option 3, Ibn al-Arabi, is also not the correct answer because although he was a renowned Sufi philosopher, his teachings primarily emphasized spiritual realization and the concept of unity of existence, rather than the specific idea of `Farr-i Izadi` that was influential in shaping the Mughal kingship.

- Option 4, Bayazid Bistami, is not the correct answer either because he was an early Sufi mystic from the 9th century, and his teachings primarily focused