Did you recently apply for a CC? The bank will look into your credit report and say 'Your commitment is higher than your income. Which means you are likely to default on your card. That is why banks reject you! It is a good idea not to apply at this time, try again in 6 months time. Of course, at that time there must be a change in circumstances, you have to demonstrate that your income ( on record of course, the bank won't believe your parent is paying the loan!) could support your commitment . If not, your only chance then to get the card is to pledge FD.

Preferably the bigger branch, where staff have better experience dealing with this sort of application. But do you intent on pledging FD now? Not a good idea though. It's better to cool off 6 months before you apply again.