Please Help Me Out From This Situation

First, you must realise that you have taken over the job of the admin person. He used to have all the power in the company being in charge of HR and therefore deciding leave approvals, late records, etc. naturally he does not like you and never will.

Secondly, he is wrong. Your job and responsibility is towards the company and its benefits. He is not paying your salary, the company is. You will always think of the company benefit not employees. All benefits given to employees is also only for benefit of employer, in keeping employees satisfied and efficient. So, follow the law. If it requires 21 days leave, by all means, allow it. Don't go beyond that unless it's industry standards and therefore required to retain employees.

You are not there to win a popularity contest. You are going to be required to implement rules and policy. You can't do that being very friendly. If you do, you will be constantly under pressure to compromise. Instead it may be better to maintain a distance (by all means be polite and rational).

Those who think HR is there to control are the ones who have misused the privileges and lack of control in the past. If the changes you made haven't given them the clues,mother they won't get it anyway. Forget it, don't try to be friendly, just do your work.

And in case of rude behaviour, you need to decide at what point you need to go and discuss this with your boss (I assume he is the owner).

When I worked in the Productivity Services, a Service function like the HR, an advice given while training was to be friendly but not familiar with the staff. I am sure that holds good for HR people too.

Everyone feels the same frustration in initial days at their organization. The bitter truth is they won't allow you to implement your ideas. The reason is they fear change. They are too rigid to come out of their comfort zones.
You mentioned the word fighting, but that leads to mistrust and negative competition.
The only way to win over them is to mingle with them, study their behaviour, be a good colleague, earn their trust by helping at all levels. They start listening to you. Then you may have proper stage to showcase your ideas.
It takes at least one year time.
Don't be hasty. Good Luck.