Just curiuos to know what is the benefit for the bitcoin mined few years back as compared to the ones recently mined?
The price of both of them will be the same.
Why would anyone want old minted BTC

It could be tax fraud or money laundering.
Someone else will pay the price.
Tax avoidance would be my guess.
Here in the US, long term capital gains are capped at 20% short term are above 35% once you hit $210,000
It's also easier to hide other trades / gains. If you have 5
BTC that has not moved in 5 years and the IRS looks at you, they may or may not dig deeper.
If you have 5
BTC that you accumulated over the last year they are going to crawl through every thing you did to make sure your are paying everything on every trade.
-Dave
This would be my guess. The OP claims the bitcoin he has is "freshly mind," and it would be easy enough to confirm if that's true or not. There must be something motivating the OP to "pay a premium." Obviously anyone looking to deal with the OP should take every precaution to make sure that the coins they're receiving weren't obtained through some criminal activity.