As already mentioned by one Member, it is possible to get Government jobs in countries like USA where qualifications and experience matter most. So, you need to specialize in a particular field and then find out ways and means of getting a Government job. For example, there are economists from India, who have worked with foreign Governments or Govt-aided institutions like World Bank, UNICEF, etc.
To the best of my knowledge, there are specific rules in each country, and it may be difficult to know such rules right away. You need to explore the possibilities through your contacts or by contacting the embassy officials who might guide you to some extent.
The second part of the question relates to getting Government jobs in Banking, which means either the Reserve Bank of India, or any of the Public Sector Banks. Please do note that these banks have an entrance examination followed by interview. It is so easy to get full details about such vacancies if you can approach any coaching center for bank examinations in your town or city. They will be fully aware of such vacancies, the minimum eligibility conditions and so on. Once you get the information, it will be much easier for you to apply and get the job.