Hi Sinann,
Patrick's fathers name is from his marriage in India in 1848. I also suspect he had a brother, Michael. As on the baptism of his son, James (1851, Madras) he (Patrick jnr) stands proxy for a Michael Whyte. I would presume as a godfather.
I'm not familiar with the Applotment books, I'll have to do some reading, so not sure if they list whole family's or just the tenant.
Now, I'm going to ask you a BIG question

If this was your piece of research where would you start looking for Patrick's baptism? Just as an aside, I think the family might have been Church of Ireland as opposed to RC as on his son's RN service record he states, C of E,
Jane