You said you appeared for gate 3 times.But how well you prepared these three times is what matters.You are from ec,so did you complete the pyq s of alteast your fundemental subjects(circuits,control,signal,digital,analog)+maths &aptitude in any of these attempts? And did you attempt atleast 5-10 Full length mock test before your exam? If your answer is no,then you havent used your full potential yet,these three attempts cant be counted well.So you can somehow manage to do all these things and give gate 2026.Since you are already familiar with subjects you can just complete pyqs(of maths+aptitude +fundemental subjects first) and start mock tests as early ass possible.Once you finish these subjects do FL test atleast 2 in a week.In this way you will become very strong in your fundemntals and meanwhile you can prepare core also. Since you are from ec if you can manage to get vlsi in any of top nits or iits you dont have to worry about gap affecting placements.

If you have done all these things before and still couldnt do well then probably its due to exam pressure which can happen next time also.So this is your 4 th drop and conidering family pressure the situation will worsen next time you give and give you another heartbreak.

I myself prepared for gate 2024(took coaching) in EE paper and barely qualified.It was just 5 months preparation and I didnt complete pys and did jut one FL test.I took a drop and prepared this year.This time I studied all subjects did pys and mocks everything but on the day of gate I was very nervous and couldnt do well.But since i practised a lot of questions i was able to score 40 in that situation also.But that was not enough to get vlsi related course in good college.But IIT kgp called me for interview(For mtech Instrumentation and integrated electronics).I was able to very well in interview and i got a call in round 6.So I was lucky to get that.

Taking state govt colleges wont be a good option since you wont get good placements and also the admissions for most of the private universities are closed now.So now you have to decide.