Traditionally, the Cardinal Secretary of State represented the number two authority in the Vatican. This official and his department, the Secretariat of State, had wide authority over both foreign affairs and financial matters.
However, in 2014, this role was re-organized, with the Secretary of State keeping the foreign affairs responsibilities (much like the US's Secretary of State) while the financial roles were consolidated into the new Secretariat for the Economy, with George Pell as its first prefect.
In this sense, since the Cardinal Secretary of State was the old number two, the Prefect of the Secretariat for the Economy could be considered the number 3 job.
However, there are other job titles that could be considered of at least equal importance with those mentioned. Other contenders could be the President of the Pontifical Commission for Vatican City State, which is the president of the legislature; the Camerlengo, who administers the Vatican City and acts as acting Head of State during a Papal interregnum, or the Dean of the College of Cardinals, who is the second most senior member of the Catholic Church.