The phrasal verb "sit on sth" means "to be a member of a group of people". Well, according to Longman, "to sit in / on sth" means "to be a member of a committee, parliament, or other official group", the same thing. I don't know why my phrasal verbs book "says" just "sit on sth" and doesn't say the "in" too. Perhaps Parliament can only be used with "in" with this meaning, I don't know. When I found the meaning of "sit on sth" for the first time, I realised that I could say "To sit on a Parliament" and not "To sit in a Parliament". Is my phrasal vebs book incomplete? Can "sit on a Parliament" be correct? I hope you understand my question.
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Neither of “sit in a Parliament” and “sit on a Parliament” are correct. Both are wrong. (See added note.) The proper phrase is “sit in Parliament”. Eg, see ngrams for sit in a Parliament,sit on a Parliament,sit in Parliament.
(Added note: More precisely, both are usually inappropriate as a way of saying that someone is a Member of Parliament. They are not grammar mistakes. While some examples of use of “sit in a Parliament” and “sit on a Parliament” may be found – as noted in FumbleFingers' answer – neither phrase is a customary English-language way to say that a person is a Member of Parliament.)
Phrase “sit on a jury” is common. In common parlance it means to participate as a member of a jury, but – to digress – in Tenniel's illustration for Alice in Wonderland, Alice appeared to sit on a jury without being a member of it:
(Actually, it was merely that “she jumped up in such a hurry that she tipped over the jury-box with the edge of her skirt, upsetting all the jurymen on to the heads of the crowd below”, rather than sitting on the jury.)
Those Anglophones who have a Parliament (mine being the mother of all, loosely speaking) don't usually refer to it using an article. Their elected representatives just sit in Parliament, as jwpat says.
Not that this means sit on a parliament is "incorrect" in any meaningful sense. There are no grammatical rules involved. It's just established custom and practice.