Hi Aspirant,

You can start studying for government exams right after entering into third year of your engineering. You can start preparing for exams in this duration.Since by this time you will be able to understand the subjects and syllabus of your stream , it would be easy for you to start preparing for some government exams like GATE, UPSC,etc.By the time you will be fulfilling the eligibility criteria you would be already prepared to give exams.
You can also check the link below for some other competition exams reference
https://competition.careers360.com/
Hope this helps.
Thank You!