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Credit cards were easy to come by for teenagers and youngsters. But recent regulations have changed that and made a minimum age of 21 years mandatory to be eligible for a credit card alone. The reason why such a change has been implemented is mainly out of one concern. A lot of banks have been targeting college freshmen in credit card campaigns and they have been running into debts which the parents have to repay. Since you have been denied a card on various occasions and you are only 18 years old you cannot apply for and get a card on your own.
From your query it is also clear that your need for the card is to establish a good credit history. Keeping that in mind there are steps you can take to go about it. Firstly what you can do is to have a regular checking account opened with a bank. You can get a letter of introduction to do so from your parents or older friends for this. When you maintain a good record with the bank they will be more willing to let you have a prepaid credit card. You can also deposit a certain amount of money to get a secured credit card and then make very minimal payments which you can pay off every month to work on your credit history. Your deposit amounts will be held as collateral in the event of your being unable to pay on purchases.
In most cases of applicants being under 21, there is no exemption except maybe for some banks that have tie-ups with the university you are at and is offering you a credit card. If an exemption is made to someone under 21 it is only if they can show proof of income which makes them able to pay their bills and afford a credit card. There are also department store credit cards which are available for amounts as low as the limit you have mentioned. These can also be used to build a semblance of credit history before applying for a credit card with low limits to start off with. If you can get a parent to co-sign on your credit card application then getting the card will be much easier and it is almost always approved.