You are doing the right thing by getting a Credit Card to maintain your Credit Score. However, you have to use it responsibly by paying your total balance on time, every time. This will help you maintain a high score.
Coming to your other query, we have plenty of Credit Cards with zero annual fees. Here are some of them.
• Kotak Royal Signature Credit Card - This Credit Card has some stellar features like fuel surcharge waiver, access to premium airport lounges, and priority assistance. The card comes in two variants – paid and free. You can pick either one based on your budget and spending needs. Annual Fee is nil for the first year and Rs. 999 for the second year. APR – 37.2% per annum
• Jet Airways IndusInd Bank Voyage Visa Card – This one comes with a unique reward structure and you earn JPMiles on every travel-related spend. This card also has you covered with exciting offers on lifestyle, shopping and dining spends even when you are not travelling. Annual Fee is nil for the first year and Rs. 2,000 for the second year. APR – 46% per annum
• HSBC Visa Platinum Card – This is a lifetime free Credit Card. It’s packed with deals offered on shopping, dining and travel along with a host of other benefits and features. Annual Fee will be nil. APR – 39.6% per annum
Read this blog post for more information – Credit Cards With Zero Annual Fees.
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