Notaries aregoverned by the Notaries Act 1952, which mentions their powers,duties and functions. It isa public office and can come under the definition of 'authority'.
There is no adjudicatory or resolution of disputes role assigned to a Notary. A quasi-judicial or judicial authority, or a statutory forum under the Consumer Protection Act or tribunals and comittees constituted under statutes, have such roles assigned and for limited purposes as mentioned in the statute, such bodies are deemed as 'courts'. Bodies like Ombusman, industrial tribunal,arbitral tribunal etc too have adjudicatory roles but beyond powers to administer oath and receive evidence, they do not have the status of courts
Only the Supreme Court, High court,and civil and criminal courts in subordinate judiciary are courts in India.