When you say no overdraft, you should mean the kind of card that saves money first and then spends it. The card of ICBC seems to be called Pig Fuka. I wonder if I can do it now. Citic has a kind of card called blue card, which is the same, and it takes the existing discount in different places.
Generally, applying for a credit card at a bank outlet requires ID cards, proof of income and other documents, especially proof of income, which is quite troublesome. If possible, you can find street vendors to sell cards through them, and generally do not need proof of income.