Should I leave my placement in Tata Steel from NIT Jamshedpur and go to Delhi for the GATE preparation and getting into PSUs?

Honestly, I wouldn’t suggest you forgo the offer from Tata Steel as it’s not everyone one gets to work in that prestigious company. In my opinion, I should try working there for at least a year and prepare for GATE also. You can go to the educational hubs, write mock exams, and give GATE in the coming year. If you manage to get a decent rank in GATE, you can resign and go for a PSU. But if you don’t then you will have a stable job already. 

However, if you are very keen to get into a PSU, then resign from your current job and go to Delhi for full-time preparation. If you are to get a PSU well and good but if you don’t remember you have an experience of 1 year at Tata Steel that will help you. 

Make a wise decision after considering all the factors!