MY SCORE IS 564 MECHANICAL. WHAT I CAN DO FURTHER?

As per your score and previous year cutoff, the colleges you get in first round are:-

National Institute of Technology Mizoram Department of Mechanical Engineering Thermal Engineering

Motilal Nehru National Institute of Technology Allahabad Department of Applied Mechanics Biomedical Engineering

National Institute of Technology Srinagar Department of Mechanical Engineering Industrial Tribology & Maintenance Management

Sant Longowal Institute of Engineering and Technology Department of Mechanical Engineering Manufacturing System Engineering

Shri Mata Vaishno Devi University Katra School of Mechanical Engineering Manufacturing & Automation

Sant Longowal Institute of Engineering and Technology Department of Mechanical Engineering Welding & Fabrication

To know more about your chances of getting other colleges check out the PSU/college predictor link below:

https://engineering.careers360.com/gate-college-predictor