Okay, so let's play with this hypothetical situation then.
Your half brother says your mum told him that when she inherited, she would give him half.
He's sort of claiming there was a verbal contract right?
Except she never inherited. You did. So there's no agreement, no contract, and you're not legally or morally obligated to give him anything.
In this situation, point out he never gave you any of his inheritance. When he bleats 'but your mum agreed!' - mention the above. See what he says. I'd be very curious to know.
Also, he sounds very dogged in his focus on your money. you should know that even if you try and pacify him with 'some' money, his eye is on the prize of half. it won't make him go away just palming him off with anything less than that. He wants half.
You're going to have to dig deep within yourself and say no to anything. Let him threaten you with legal action, and I guarantee you once he starts making calls to solicitors they will put him straight. Very straight.
I can't bear CFs like this. Please don't give him anything.