Can Naturalized citizen hold public office?

There is no such thing as an unnaturalized citizen

A natural-born US citizen is someone who was born in the USA.

A naturalized US citizen is someone who was born somewhere other than the USA, but chose to become a US citizen. (This person applied for citizenship, lived in the US as a law-abiding citizen for the required number of years, passed the test, took the oath, and was sworn in as a naturalized citizen with the rights and responsibilities as a natural-born citizen.

A naturalized-citizen can run for any office except President of the United States.

The president must be a natural born ciitizen.