Hello, 

As you have mentioned that your wbjee rank is 62944 which is not that good to fetch any seat. But if we look over previous year's cutoff for wbjee for general category, you may get the colleges mentioned belowuunder home state quota :

• Jadavpur University, Kolkata. For metallurgical engineering, power engineering, printing engineering, production engineering. 
• Heritage Institute of Technology, Kolkata. For Applied Electronics & Instrumentation Engineering, Biotechnology, civil engineering, electrical engineering, mechanical engineering.
• Narula Institute of Technology, Agarpara for Applied Electronics & Instrumentation Engineering, civil, mechanical, electrical and computer science engineering.
• Academy of Technology, Hooghly. 
• Bengal Institute of Technology, Kolkata
• Haldia Institute of Technology, Haldia
• Kalyani Government Engineering College, Nadia
• Jalpaiguri Government Engineering College, Jalpaiguri
• Techno India University, Kolkata
• University Institute of Technology, The University of Burdwan, Burdwan

For furthermore  Information please go through the link given below to predict the colleges you may get :

https://engineering.careers360.com/articles/wbjee-cutoff. 

I hope this would help you. For further queries please feel free to write me down in the comment box. 

Careers360 presents the college predictor of WBJEE 2019 which will help candidates list down the colleges for which they will be eligible according to their performance in the examination. WBJEE 2019 college predictor has been activated. To use the college predictor, the candidates will be required to submit their WBJEE ranks, preferences and more information. The list of colleges according to chances of admission will be listed by the college predictor of WBJEE 2019

https://www.careers360.com/wbjee-college-predictor