Suit for partition can be filed by any person who has a share in the property, either a coparcener or legal heir who has a contingent or vested interest in the property can file the suit in a civil court. It is filed after serving the legal notice to the other legal heirs.
While Letters of Administration is issued by a competent jurisdiction under the Indian Succession Act,1925. It is a legal instrument to distribute the estate of the deceased to the descendants. It is issued when the will of the deceased has no executors.
Please refer the below link for more details on Law relating to succession.
Hope this answers your query.