Assuming the company knew your abilities (or lack thereof) when they hired you, you have nothing to worry about.
Keeping your job is not about being the best. It's about meeting expectations.
If your company expected you to be a fresh grad with some decent skills but a lack of experience, and you turn out to be a fresh grad with decent skills and a lack of experience, then they hired the person they wanted and they're absolutely not going to fire you.
Finding competent people is hard. Finding people who can actually get stuff done, who are honest, competent and pleasant to be around, is really hard. If you're competent, pleasant to be around and you proactively strive to keep learning and gain more skills/experience, you're a lot rarer (and more valuable in the long run) than you might imagine.
So far as getting rid of your fear: Communicate with your boss. Tell them how you feel, and they'll tell you if you're meeting their expectations or not (clue: if you weren't, you'd already know about it).
I interned for my current employer for a few months before Uni, doing data entry. Then I went off to Uni, discovered some hitherto undiagnosed mental health problems and completely imploded. I went back to my old employers and said (paraphrasing) "This is what happened. This is where I am. I'm looking for a job, would you be willing to hire me?". Throughout the next year, my attendance at work was erratic, culminating in 6 months of long-term sick leave. I'm mildly autistic, and made any number of social faux pas trying to figure out how the hell people are supposed to behave around one another. I don't conform well to rules and I'm not great at sticking to rigid schedules.
I'm also still employed.
I'm still employed because they knew what they were getting in to when they offered me a job. I never hid anything, I never misrepresented myself, and so, when things didn't go well, it was already factored in to their expectations.
So, to reiterate: It doesn't matter how good/bad you are on an absolute scale, what matters is your employer's expectations and whether you are who they expected you to be.