Having a degree in Economics won't hinder your pursuit of Archaeology.  .It's commendable that you are following your interest in history and archaeology. While Economics is valuable, a career fueled by passion can be very rewarding.

Many universities and colleges in India offer diploma courses in Archaeology. These programs typically last for one or two years, depending on the institution. Since you have a diploma in Mechanical Engineering (though with a backlog) and higher secondary education with History and Geography, you'd likely be eligible for most Diploma in Archaeology programs. They might require a minimum percentage in your higher secondary exams, so check with specific colleges.

Your Economics background can be surprisingly beneficial in Archaeology:

• Data Analysis: Archaeological research often involves analyzing large datasets from excavations and surveys. Your Economics background could be an asset in this area.
  
  
• Resource Management: Archaeology projects require budgeting and resource management skills, which your Economics knowledge can help with.
  
  Choose the Right Program: Look for Diploma programs with a strong focus on fieldwork and research. Many programs include practical components like excavation simulations or archaeological site visits.
  
  Highlight Your Interests: During the application process, highlight your passion for fieldwork and research in your statement of purpose.
  
  I hope it helps!