unsecured card for students

There are no unsecured cards for "students". You need to apply as "self employed" if you are not salaried. You can try Flipkart axis or amazon icici as these co-branded cards have high approval rate even for the beginners with no income proof. Do not apply core cards from ICICI or HDFC without prior relationship.

Pre-approved is the only option or you can apply as self employed, but still income proof would be required in majority cases.

While I was a student, I was able to get these credit cards -

Kotak Aqua, now called Kotak 811 (FD based)

IDFC Onecard (pre-approved basis cibil score)

IDFC Millennia (pre-approved basis onecard cc)

IDFC Wealth (offered on onecard closure)

ICICI Amazon (no income proof asked)

ICICI Makemytrip (pre-approved basis amazon cc)

Axis Flipkart (no income proof asked)

Axis Magnus (applied C2C basis makemytrip cc)

SBI Simplyclick (no income proof asked)

HDFC Millennia (pre-approved basis savings ac)

HDFC Tata Neucard+ (pre-approved basis millennia cc)

I suggest u to open HDFC digi account (5k mab), maintain just more than min balance in 6 months u may get. Take  advantage of fyf millennia debit card.

Holding 14 credit cards from 9 different banks never given any income proof for any of my cards. CIBIL 780+