Meaning
A very small sum of money — historically a small coin worth a penny-halfpenny in the old currency. 'Not a red quattie' means not a single cent, the very least amount there is, and 'a quattie worth' is the tiniest bit you could buy at the shop. Though the coin is long gone, the word lives on in these expressions for next to nothing, a measure of how little money one has, and it belongs with 'gill' among the old small-money terms of Jamaican trade.
Examples
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Mi nuh have a red quattie.
I don't have a single cent.
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It nuh cost but a quattie back inna di day.
It only cost a penny-halfpenny back in the day.
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Him nah spend a quattie pon it.
He won't spend a penny on it.
Origin
From Spanish 'cuarto' (a quarter), for a small colonial-era coin; it lived on in Jamaican speech as the word for a tiny amount of money.
How it’s used
Now used figuratively for 'the smallest bit of money'. 'Not a red quattie' is the emphatic way of saying 'no money at all'.